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

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