
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 square  $ABCD$  is given. A point  $P$  is chosen inside the triangle  $ABC$  such that  $\angle CAP = 15^\circ = \angle BCP$ . A point  $Q$  is chosen such that  $APCQ$  is an isosceles trapezoid:  $PC \parallel AQ$ , and  $AP=CQ, AP\nparallel CQ$ . Denote by  $N$  the midpoint of  $PQ$ . Find the angles of the triangle  $CAN$ .

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