
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
Points \( A, B, C \) lie on a circle centered at \( O \) with radius 7. The perpendicular bisector of \( AB \) meets the segment \( BC \) at \( P \) and the extension of \( AC \) at \( Q \). Determine the value of \( OP \cdot OQ \).

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