
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
Origami. Mitya is going to fold a square sheet of paper $ABCD$. Mitya calls a fold beautiful if the side $AB$ intersects the side $CD$ and the four resulting right triangles are equal.

Before this, Vanya selects a random point $F$ on the sheet. Find the probability that Mitya can make a beautiful fold passing through the point $F$.

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