
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 $f(x)=2\sin x\cos x-\sin ^{2}x-3\cos ^{2}x+1$.
(1) Find the interval(s) where the function $y=f(x)$ is monotonically increasing.
(2) If the function $y=f(x)$ has exactly 3 zeros in the interval $[0,a]$, find the range of values for the real number $a$.

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