
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 $f(x)=2\sin x(\sin x+\cos x)$, $x\in R$.
(I) Find the interval where the function $f(x)$ is monotonically increasing;
(II) If $f(\frac{a}{2})=1+\frac{3\sqrt{2}}{5}$, $\frac{3\pi}{4}<a<\frac{5\pi}{4}$, find the value of $\cos a$.

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