
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 $\triangle ABC$ have three interior angles $A$, $B$, and $C$. Given vectors $m = (\sin A, \sin B)$ and $n = (\cos B, \cos A)$, if $m \cdot n = 1 + \cos(A + B)$, then $C =$ (　　)

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