
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, the sides opposite to angles A, B, C are a, b, c respectively, and $2a\cos C=2b-c$.
(1) Find the measure of angle A;
(2) If triangle ABC is an acute triangle, find the range of $\sin B+\sin C$;
(3) If $a=2 \sqrt {3}$, and the area of triangle ABC is $2 \sqrt {3}$, find the value of $\cos 2B+\cos 2C$.

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