
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
Let  $ABCD$  be a convex quadrilateral with  $\angle{DAC}= \angle{BDC}= 36^\circ$  ,  $\angle{CBD}= 18^\circ$  and  $\angle{BAC}= 72^\circ$ . The diagonals and intersect at point  $P$  . Determine the measure of  $\angle{APD}$ .

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