
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 that the domain of $f(x)$ is $(0, +\infty)$, satisfying $f(x) > 0$, and $f′(x)$ is its derivative, $\frac{f′(x)}{f(x)} < -1$.  
(Ⅰ) Discuss the monotonicity of the function $F(x) = e^x f(x)$;  
(Ⅱ) Let $0 < x < 1$, compare the magnitude of the function $xf(x)$ and $\frac{1}{x}f\left(\frac{1}{x}\right)$.

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