
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 $f(x)=\sin x+\cos x$, $f'(x)$ is the derivative of $f(x)$.

(1) Find the smallest positive period of the function $F(x)=f(x)\cdot f'(x)+f^2(x)$;

(2) If $f(x)=2f'(x)$, find the value of $\dfrac{1+\sin^2x}{\cos^2x-\sin x\cdot \cos x}$.

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