
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 a triangle $\triangle ABC$ with angles $A$, $B$, $C$ and their respective opposite sides $a$, $b$, $c$, and a function $f(A)=2\sqrt{3}\sin A\cos A-2\sin^{2}A+2$.

(1) If $f(A)=2$, find the measure of angle $A$.

(2) If $a=3$, and vectors $m=(1,\sin C)$ and $n=(2,\sin B)$ are collinear, find the value of $b+c$.

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