
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$, respectively, and $\sin B(\sin C+ \sqrt {3}\cos C)- \sqrt {3}\sin A=0$, $b= \sqrt {3}$.
(1) Let the perimeter of $\triangle ABC$ be $L=f(A)$, find the expression for $f(A)$ and the maximum value of $L$.
(2) If $a+c=2$, find the area of $\triangle ABC$.

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