
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 acute triangle $ABC$, the sides $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively, satisfy $\cos (A-C)-\cos (A+C)=\sqrt{3}\sin C$.

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

(2) If $b=\sin B$, and the area of $\triangle ABC$ is $\frac{3\sqrt{3}}{16}$, find the value of $b+c$.

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