
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 that point \( P(-2,5) \) lies on the circle \( C: x^{2}+y^{2}-2x-2y+F=0 \), and the line \( l: 3x+4y+8=0 \) intersects the circle at points \( A \) and \( B \), find \( \overrightarrow{A B} \cdot \overrightarrow{B C} \).

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