
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
In an acute-angled triangle  $ABC$  on the side  $AC$ , point  $P$  is chosen in such a way that  $2AP = BC$ . Points  $X$  and  $Y$  are symmetric to  $P$  with respect to vertices  $A$  and  $C$ , respectively. It turned out that  $BX = BY$ .  Find  $\angle BCA$ .

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