
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 $f(x)=2\sin^{2}\left( \frac{π}{4}+x\right)- \sqrt{3}\cos 2x$,

(1) Find the smallest positive period and the monotonic intervals of $f(x)$.

(2) When $x\in\left\[ \frac{π}{4}, \frac{π}{2}\right\],$ find the maximum and minimum values of $f(x)$.

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