
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
Right triangle  $ABC$  is inscribed in circle  $W$ .  $\angle{CAB}=65$  degrees, and  $\angle{CBA}=25$  degrees. The median from  $C$  to  $AB$  intersects  $W$  and line  $D$ . Line  $l_1$  is drawn tangent to  $W$  at  $A$ . Line  $l_2$  is drawn tangent to  $W$  at  $D$ . The lines  $l_1$  and  $l_2$  intersect at  $P$ Determine  $\angle{APD}$ 

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