
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 $$f(x)= \frac {(sinx-cosx)sin2x}{sinx}$$.
(I) Find the domain of definition of $f(x)$ and the smallest positive period $T$;
(II) Find the range of $x$ such that $f(x) \geq 0$;
(III) Is there a smallest positive real number $m$ such that shifting the graph of the function $f(x)$ to the left by $m$ units makes it an even function? If it exists, find the value of $m$; if not, please explain why.

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