
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
Let \( \mathrm{E} \) be the midpoint of side \( \mathrm{AB} \) of square \( \mathrm{ABCD} \). Points \( P \) and \( Q \) are randomly selected on sides \( \mathrm{AD} \) and \( \mathrm{BC} \) respectively. What is the probability that \( \angle \mathrm{PEQ} \) is an acute angle?

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