
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 $f(x)=2\sin ^{2}(\frac{\pi }{4}+x)-\sqrt {3}\cos 2x$.
(1) Find the minimum positive period and the interval of monotonic increase of $f(x)$;
(2) If the equation $f(x)-m=2$ has a solution for $x\in [\frac{\pi }{4}, \frac{\pi }{2}]$, find the range of real number $m$.

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