
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 $f(x)= \sqrt {3}\sin ωx\cos ωx- \cos ^{2}ωx- \dfrac {1}{2}(ω > 0,x∈R)$, the distance between two adjacent highest points on its graph is $π$.
(I) Find the interval where the function $f(x)$ is monotonically increasing.
(II) In triangle $△ ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, where $c= \sqrt {7}$, $f(C)=0$, and $\sin B=3\sin A$. Find the values of $a$ and $b$.

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