<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>
## Description

A pole is attached by an un-actuated joint to a cart, which moves along a frictionless track.
The pendulum is placed upright on the cart and the goal is to balance the pole by applying forces
 in the left and right direction on the cart.

## Action Space

The action is a `ndarray` with shape `(1,)` which can take values `{0, 1}` indicating the direction
 of the fixed force the cart is pushed with.

- 0: Push cart to the left
- 1: Push cart to the right

**Note**: The velocity that is reduced or increased by the applied force is not fixed and it depends on the angle
 the pole is pointing. The center of gravity of the pole varies the amount of energy needed to move the cart underneath it

## Observation Space

The observation is a `ndarray` with shape `(4,)` with the values corresponding to the following positions and velocities:

| Num | Observation           | Min                 | Max               |
|-----|-----------------------|---------------------|-------------------|
| 0   | Cart Position         | -4.8                | 4.8               |
| 1   | Cart Velocity         | -Inf                | Inf               |
| 2   | Pole Angle            | ~ -0.418 rad (-24°) | ~ 0.418 rad (24°) |
| 3   | Pole Angular Velocity | -Inf                | Inf               |

**Note:** While the ranges above denote the possible values for observation space of each element,
    it is not reflective of the allowed values of the state space in an unterminated episode. Particularly:
-  The cart x-position (index 0) can be take values between `(-4.8, 4.8)`, but the episode terminates
   if the cart leaves the `(-2.4, 2.4)` range.
-  The pole angle can be observed between  `(-.418, .418)` radians (or **±24°**), but the episode terminates
   if the pole angle is not in the range `(-.2095, .2095)` (or **±12°**)

## Rewards

Since the goal is to keep the pole upright for as long as possible, a reward of `+1` for every step taken,
including the termination step, is allotted. The threshold for rewards is 500 for v1 and 200 for v0.

## Starting State

All observations are assigned a uniformly random value in `(-0.05, 0.05)`

## Episode End

The episode ends if any one of the following occurs:

1. Termination: Pole Angle is greater than ±12°
2. Termination: Cart Position is greater than ±2.4 (center of the cart reaches the edge of the display)
3. Truncation: Episode length is greater than 500 (200 for v0)

## 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>