
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 $f(x)=\cos x\cos (x+ \frac {π}{3}).$
(I) Find the smallest positive period of $f(x)$;
(II) In $\triangle ABC$, angles $A$, $B$, $C$ correspond to sides $a$, $b$, $c$, respectively. If $f(c)=- \frac {1}{4}$, $a=2$, and the area of $\triangle ABC$ is $2 \sqrt {3}$, find the value of side length $c$.

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