
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
A circle is circumscribed around a right triangle $\mathrm{ABC}$ with hypotenuse $\mathrm{AB}$. A point $\mathrm{P}$ is marked on the longer leg $\mathrm{AC}$ such that $\mathrm{AP} = \mathrm{BC}$. The midpoint of the arc $\mathrm{ACB}$ is marked as $\mathrm{M}$. What can the angle $\angle \mathrm{PMC}$ be?

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