
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 $K$ be the incenter of $\triangle ABC$. Points $C_1$ and $B_1$ are the midpoints of sides $AB$ and $AC$ respectively. Line $AC$ intersects $C_1K$ at point $B_2$, and line $AB$ intersects $B_1K$ at point $C_2$. If $\triangle AB_{2}C_{2}$ has the same area as $\triangle ABC$, find the measure of $\angle CAB$.

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