
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 the function $f(x)=\cos(2x- \frac {4\pi}{3})+2\cos^{2}x$.  
(1) Find the maximum value of the function $f(x)$;  
(2) Given triangle $\triangle ABC$ with interior angles $A$, $B$, and $C$, if $f(B+C)= \frac {3}{2}$, find the value of angle $A$.

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