
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 $f(x)=2\sin x\cos x+2\cos ^{2}x$.
(1) Find the interval where the function $f(x)$ is monotonically increasing;
(2) After shifting the graph of the function $y=f(x)$ to the right by $\frac{\pi}{4}$ units, we obtain the graph of the function $y=g(x)$. Find the solutions to the equation $g(x)=1$.

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