
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
The angles  $A$  and  $B$  of base of the isosceles triangle  $ABC$  are equal to  $40^o$ . Inside  $\vartriangle ABC$ ,  $P$  is such that  $\angle PAB = 30^o$  and  $\angle PBA = 20^o$ . Calculate, without table,  $\angle PCA$ .

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