<system>
You are an experienced Python developer. You will be provided with an incorrect code snippet from a Python program. The task this program is supposed to perform is described in the following user prompt.
Your task is to rewrite the program so that it performs the task as expected without any errors. You will be rewarded based on the number of test cases your code passes.
</system>

<user>
The Taxi Problem involves navigating to passengers in a grid world, picking them up and dropping them
off at one of four locations.

## Description
There are four designated pick-up and drop-off locations (Red, Green, Yellow and Blue) in the
5x5 grid world. The taxi starts off at a random square and the passenger at one of the
designated locations.

The goal is move the taxi to the passenger's location, pick up the passenger,
move to the passenger's desired destination, and
drop off the passenger. Once the passenger is dropped off, the episode ends.

The player receives positive rewards for successfully dropping-off the passenger at the correct
location. Negative rewards for incorrect attempts to pick-up/drop-off passenger and
for each step where another reward is not received.

Map:

        +---------+
        |R: | : :G|
        | : | : : |
        | : : : : |
        | | : | : |
        |Y| : |B: |
        +---------+

## Action Space
The action shape is `(1,)` in the range `{0, 5}` indicating
which direction to move the taxi or to pickup/drop off passengers.

- 0: Move south (down)
- 1: Move north (up)
- 2: Move east (right)
- 3: Move west (left)
- 4: Pickup passenger
- 5: Drop off passenger

## Observation Space
There are 500 discrete states since there are 25 taxi positions, 5 possible
locations of the passenger (including the case when the passenger is in the
taxi), and 4 destination locations.

Destination on the map are represented with the first letter of the color.

Passenger locations:
- 0: Red
- 1: Green
- 2: Yellow
- 3: Blue
- 4: In taxi

Destinations:
- 0: Red
- 1: Green
- 2: Yellow
- 3: Blue

An observation is returned as an `int()` that encodes the corresponding state, calculated by
`((taxi_row * 5 + taxi_col) * 5 + passenger_location) * 4 + destination`

Note that there are 400 states that can actually be reached during an
episode. The missing states correspond to situations in which the passenger
is at the same location as their destination, as this typically signals the
end of an episode. Four additional states can be observed right after a
successful episodes, when both the passenger and the taxi are at the destination.
This gives a total of 404 reachable discrete states.

## Starting State
The episode starts with the player in a random state.

## Rewards
- -1 per step unless other reward is triggered.
- +20 delivering passenger.
- -10  executing "pickup" and "drop-off" actions illegally.

An action that results a noop, like moving into a wall, will incur the time step
penalty. Noops can be avoided by sampling the `action_mask` returned in `info`.

## Episode End
The episode ends if the following happens:

- Termination:
        1. The taxi drops off the passenger.

- Truncation (when using the time_limit wrapper):
        1. The length of the episode is 200.

## Class Definition
The class should be called "Environment". It should have at least:

- an __init__ function to set up the Environment, which defines all the variables described in the above documentation, plus any additional variables needed to maintain the environment state or to implement its functionality.
- a set_state function to set a custom value for the environment and its internal representation (you can assume that when "set_state" is used, the task is not done and internal variables should be set as a consequence). set_state takes a single argument as input: a state observation from the observation space defined above.
- a step function to predict a step in the environment. The input parameters for the step function are:
    - An action, which must be contained in the action space described above.
  
    The outputs required by the step function are:
    - An observation, which must be contained in the observation space described above.
    - The reward for taking the action, as described in the reward definition above.
    - A boolean variable indicating if the episode is done.

## Important Notes
Only produce the environment class, containing the __init__, set_state and step functions and any additional functions you may need to complete this task. Do not write an example of how to use the class or anything else.
Be careful about edge cases.
Make sure to write all the required functions and that they have the exact names as specified in the task description. Missing or incorrectly named functions will not pass the tests and will result in a score of 0.
It is of VITAL importance that you do not leave undefined any function, but implement each of them completely.

First, write an explanation of the difference between the ground-truth transition and the step function's outputs in the example provided.
Second, point out the part of the code responsible for the incorrect prediction and why its logic is erroneous.
Third, suggest a concrete, actionable fix for it. 
Finally, fix the program in its entirety following the suggestion. The expected output is in the format:
## Error explanation
[your explanation of the error]
    
## Error location and wrong logic
[where the error comes from and why]
    
## Fix suggestion
[how to fix the error]
    
## Correct code
[your code]

## Incorrect code
You are provided with the following code snippet to fix.
```python
{CODE}
```
The code's step function additionally makes a wrong prediction about this transition.
## Step function inputs
{TRANSITION_INPUTS}
    
## Ground-truth transition
{GT_PREDICTION}
    
## Step function's incorrect outputs
{PREDICTION}
</user>