
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 $f(x)=(\sin x+\cos x)^{2}+2\cos ^{2}x-2$.
$(1)$ Find the smallest positive period and the intervals of monotonic increase for the function $f(x)$;
$(2)$ When $x\in\left[ \frac {\pi}{4}, \frac {3\pi}{4}\right]$, find the maximum and minimum values of the function $f(x)$.

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