
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
Given a circle with equation (x-1)<sup>2</sup>+(y-1)<sup>2</sup>=1, and a point P(3,2) outside the circle, draw two tangent lines from point P to the circle, with the tangent points being A and B. Find the value of cos∠APB.

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