
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
Let the function $f(x)=\cos (2x+ \frac {2\pi}{3})+2\cos ^{2}x$.  
(I) Find the maximum value of $f(x)$, and write the set of values of $x$ when $f(x)$ takes its maximum value;  
(II) Given in $\triangle ABC$, the sides opposite angles $A$, $B$, $C$ are respectively $a$, $b$, $c$. If $f(B+C)= \frac {3}{2}$ and $a=1$, find the maximum perimeter of $\triangle ABC$.

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