
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 triangle $ABC$ with sides $BC$ and $AC$, respectively. It turned out that the point symmetric to the incenter of the triangle with respect to the midpoint of $AB$ lies on the circumcircle of triangle $CT_{1}T_{2}$. Find the angle $BCA$.

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