
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
  $$ problem 2 $$  :A point  $P$  is taken in the interior of a right triangle $ ABC$  with  $\angle C = 90$  such hat $AP = 4, BP = 2$ , and $ CP = 1$ . Point  $Q$  symmetric to  $P$  with respect to  $AC$  lies on
the circumcircle of triangle  $ABC$ . Find the angles of triangle  $ABC$ .

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