
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 that the distance between two adjacent symmetry axes on the graph of the function $f(x)=-\cos ^{2} \frac {ω}{2}x+ \frac { \sqrt {3}}{2}\sin ωx$ is $\frac {π}{2}(ω > 0)$.
(I) Find the interval where $f(x)$ is decreasing;
(II) In $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively. If $f(A)= \frac {1}{2},c=3$, and the area of $\triangle ABC$ is $3 \sqrt {3}$, find the value of $a$.

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