
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 $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively. It is known that $c= \frac {7}{2}$ and the area of $\triangle ABC$ is $\frac {3 \sqrt {3}}{2}$. Also, $\tan A+\tan B= \sqrt {3}(\tan A\tan B-1)$.  
(I) Find the size of angle $C$;  
(II) Find the value of $a+b$.

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