
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 that the function $f(x)=\sin ^{2}wx+ \sqrt {3}\sin wx\sin (wx+ \frac {π}{2})(w > 0)$ has a minimum positive period of $π$.
(I) Find the value of $w$;
(II) Find the interval where $f(x)$ is monotonically increasing;
(III) Find the range of the function $f(x)$ in the interval $[0, \frac {2π}{3}]$.

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