
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 an isosceles triangle \( ABC \) with \( AB < BC \) and \( A \) as the unique vertex angle, let \( P \) be a point on the line \( BC \) located outside the segment \( [BC] \) such that \( BP = BA \). Let \( Q \) be a point on the line \( AP \) different from \( A \) such that \( CQ = CA \). If \( \widehat{QPC} = x \), what is the measure of the angle \( \widehat{PCQ} \)?

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