
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 $f(x)=2\cos ^{2}x+\cos (2x+ \frac {π}{3})$.
(1) If $f(α)= \frac { \sqrt {3}}{3}+1$, $0 < a < \frac {π}{6}$, find the value of $\sin 2α$;
(2) In acute triangle $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively; if $f(A)=- \frac {1}{2}$, $c=3$, the area of $\triangle ABC$ is $S_{\triangle ABC}=3 \sqrt {3}$, find the value of $a$.

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