
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In the following maze, each of the dashed segments is randomly colored either black or white. What is the probability that there will exist a path from side \( A \) to side \( B \) that does not cross any of the black lines?
![Maze](https://cdn.mathpix.com/cropped/2024_04_17_a143cf101bf1bb453a87g-2.jpg?height=564&width=1134&top_left_y=580&top_left_x=488)

Present the answer in LaTex format: \boxed{Your answer}
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