
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
Two circles intersect at points $A$ and $B$. Two secants passing through $A$ intersect the first circle at points $C$ and $D$ and the second circle at points $C'$ and $D'$. The lines $(CD)$ and $(C'D')$ intersect at point $P$.

Compare the angle $\widehat{CPC'}$ with the angle between the two circles.

What happens when $C$ and $D$ coincide?

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