
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 $f(x) = \cos^4x - 2\sin x\cos x - \sin^4x$,
1. Find the minimal positive period of $f(x)$;
2. Find the intervals where $f(x)$ is monotonically increasing;
3. If $x \in \left[0, \frac{\pi}{2}\right]$, find the range of $f(x)$.

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