
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 $f(x)=2\sin^{2}(\frac{π}{4}+x)-\sqrt{3}\sin(\frac{π}{2}+2x)-1, x∈R$.  
$(1)$ Find the smallest positive period and the interval of monotonic increase of the function $y=f\left(x\right)$;  
$(2)$ Find the range of the function $y=f\left(x\right)$ when $x∈[\frac{π}{4},\frac{π}{2}]$.

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