
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 $f(x)=- \sqrt{2}\sin \left(2x+ \frac{π}{4} \right)+6\sin x\cos x-2\cos ^{2}x+2$, where $x\in R$.

(1) Find the interval(s) where $f(x)$ is monotonically increasing.

(2) Find the equation of the symmetry axis of $f(x)$.

(3) Find the coordinates of the symmetry center of $f(x)$.

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