
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 $f(x)=\sin (2wx- \frac {π}{6})-4\sin ^{2}wx+2 (w > 0)$, the distance between two adjacent intersection points of its graph and the $x$-axis is $\frac {π}{2}$.
(1) Find the analytical expression of the function $f(x)$;
(2) If the graph of $f(x)$ is translated to the left by $m(m > 0)$ units to obtain the graph of function $g(x)$, which passes through the point $(-\frac{π}{3},0)$, find the monotonically increasing interval of $g(x)$ on $[- \frac {π}{6}, \frac {7π}{12}]$ when $m$ takes the smallest value.

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