
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
Aaron takes a square sheet of paper, with one corner labeled  $A$ . Point  $P$  is chosen at random inside of the square and Aaron folds the paper so that points  $A$  and  $P$  coincide. He cuts the sheet along the crease and discards the piece containing  $A$ . Let  $p$  be the probability that the remaining piece is a pentagon. Find the integer nearest to  $100p$ .

*Proposed by Aaron Lin*

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