
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
(10 points) Given a triangle $\triangle ABC$ with angles $A$, $B$, $C$ opposite sides $a$, $b$, $c$ respectively, and $b^2+c^2=a^2+bc$, find: (1) the value of $2\sin B\cos C-\sin(B-C)$; (2) if $a=2$, find the maximum value of the perimeter of $\triangle ABC$.

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