
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 $f(x) = \sin x + \cos x$, where $f'(x)$ is the derivative of $f(x)$.
(I) Find the maximum value and the smallest positive period of the function $g(x) = f(x)f'(x) - f^2(x)$.
(II) If $f(x) = 2f'(x)$, find the value of $\frac{1 + \sin^2 x}{\cos^2 x - \sin x \cos x}$.

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