
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 diagram shows a circle with centre \( O \) and a triangle \( O P Q \). Side \( P Q \) is a tangent to the circle. The area of the circle is equal to the area of the triangle.

What is the ratio of the length of \( P Q \) to the circumference of the circle?
A \( 1: 1 \)
B \( 2: 3 \)
C \( 2: \pi \)
D \( 3: 2 \)
E \( \pi: 2 \)

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