
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 the three interior angles of $\triangle ABC$ be $A$, $B$, and $C$. Given vectors $\overrightarrow{m}=( \sqrt {3}\sin A,\sin B)$, $\overrightarrow{n}=(\cos B, \sqrt {3}\cos A)$, if $\overrightarrow{m}\cdot \overrightarrow{n}=1+\cos (A+B)$, then $C=$ ______.

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