
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
In $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively. Given $\overrightarrow{m}=(\cos \frac {C}{2},\sin \frac {C}{2})$, $\overrightarrow{n}=(\cos \frac {C}{2},-\sin \frac {C}{2})$, and the angle between $\overrightarrow{m}$ and $\overrightarrow{n}$ is $\frac {\pi}{3}$
(1) Find $\angle C$;
(2) Given $c= \frac {7}{2}$, $S_{\triangle ABC}= \frac {3}{2} \sqrt {3}$, find $a+b$.

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