
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 $f(x)=\sin ^{2}ωx+2 \sqrt {3}\sin ωx\cos ωx-\cos ^{2}ωx\ (ω > 0)$, the distance between two adjacent symmetry axes of the graph of $f(x)$ is $\frac {π}{4}$.
(I) Find the value of $f(\frac {π}{4})$;
(II) Translate the graph of $f(x)$ to the left by $m\ (m > 0)$ units to obtain the graph of $y=g(x)$. If one of the symmetry centers of the graph of $y=g(x)$ is $(\frac {π}{6},0)$, find the monotonically increasing interval of $g(x)$ when $m$ takes the minimum value.

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