
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
The top side of a paper square is white, and the bottom side is red. A point F is randomly chosen within the square. Then, the square is folded so that one randomly chosen vertex coincides with point F. Find the expected number of sides of the resulting red polygon.

![](https://cdn.mathpix.com/cropped/2024_05_08_22585010b2534c7ab9ebg-14.jpg?height=515&width=512&top_left_y=1655&top_left_x=773)

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