
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 \( C \) be the circle with radius 1 and center at the origin. A point \( P \) is chosen at random on the circumference of \( C \), and another point \( Q \) is chosen at random in the interior of \( C \). What is the probability that the rectangle with diagonal \( PQ \), and sides parallel to the x-axis and y-axis, lies entirely inside (or on) \( C \)?

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