
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
In triangle ABC, point P lies on the segment BC such that BP = PC. Let $\angle APC = 2x$ and $\angle APB = 3x$. If AP = PC and AB = AC, find the measure of $\angle BAC$.
A) $\frac{170^\circ}{7}$
B) $\frac{180^\circ}{7}$
C) $\frac{190^\circ}{7}$
D) $\frac{160^\circ}{7}$

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