
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 $\Delta ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively. Given that $c=\frac{7}{2}$, the area of $\Delta ABC$ is $\frac{3\sqrt{3}}{2}$, and $\tan A+\tan B=\sqrt{3}(\tan A\tan B-1)$,

(1) Find the measure of angle $C$;

(2) Find the value of $a+b$.

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