
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 $\triangle ABC$, $a$, $b$, $c$ are the opposite sides of angles $A$, $B$, $C$ respectively. Given $\sqrt{3}\sin C-\cos B=\cos \left(A-C\right)$.

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

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

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