
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 that the circumcircle of $\triangle ABC$ has a diameter of $\frac{4\sqrt{3}}{3}$, and the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, with $C=60^{\circ}$.

1. Find the value of $\frac{a+b+c}{\sin A+\sin B+\sin C}$.
2. If $a+b=ab$, find the area of $\triangle ABC$.

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