
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
Given triangle ABC, vectors $\overrightarrow {m}$ = ($\sqrt {3}$sinA, sinB) and $\overrightarrow {n}$ = (cosB, $\sqrt {3}$cosA). If the dot product of $\overrightarrow {m}$ and $\overrightarrow {n}$ is equal to 1 + cos(A + B), find the value of angle C.

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