
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 intervals of monotonic increase for the function $y = f(x)$.  
(2) If the function $y = f(x)$ has exactly three zeros in the interval $[0, a]$, determine the range of values for the real number $a$.

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