
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 $f(x)= \frac {1}{2}-\cos ^{2}wx(w > 0)$ has the smallest positive period of $\frac {\pi}{2}$, determine the interval of monotonic increase for the function $g(x)=2\sin (2x-m)+1$ after shifting the graph of $f(x)$ to the right by $m(m > 0)$ units and then reflecting it about the origin when $m$ takes the minimum value.

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