
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  $ABC$  be a right isosceles triangle with right angle at  $A$ . Let  $E$  and  $F$  be points on A $B$  and  $AC$  respectively such that  $\angle ECB = 30^o$  and  $\angle FBC = 15^o$ . Lines  $CE$  and  $BF$  intersect at  $P$  and line  $AP$  intersects side  $BC$  at  $D$ . Calculate the measure of angle  $\angle FDC$ .

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