
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 $f(x)= \sqrt{2}\sin \left( 2x+ \frac{π}{4} \right)$.

(1) Find the equation of the axis of symmetry of the graph of the function $f(x)$;

(2) Find the interval(s) where $f(x)$ is monotonically increasing;

(3) Find the maximum and minimum values of the function $f(x)$ when $x\in \left[ \frac{π}{4}, \frac{3π}{4} \right]$.

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