
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 $\triangle ABC$, it is known that $\sqrt {3}a\sin C-c(2+\cos A)=0$, where $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively. Find:
1. The measure of angle $A$;
2. The length of the smallest side if the length of the longest side of $\triangle ABC$ is $\sqrt {13}$, and $\sin C=3\sin B$.

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