
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  $ AB$  be the diameter of a circle with a center  $ O$  and radius  $ 1$ . Let  $ C$  and  $ D$  be two points on the circle such that  $ AC$  and  $ BD$  intersect at a point  $ Q$  situated inside of the circle, and  $ \angle AQB\equal{} 2 \angle COD$ . Let  $ P$  be a point that intersects the tangents to the circle that pass through the points  $ C$  and  $ D$ .

Determine the length of segment  $ OP$ .

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