
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  $T_1$  and  $T_2$  be the points of tangency of the excircles of a triangle  $ABC$  with its sides  $BC$  and  $AC$  respectively. It is known that the reflection of the incenter of  $ABC$  across the midpoint of  $AB$  lies on the circumcircle of triangle  $CT_1T_2$ . Find  $\angle BCA$ .

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