
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 $f(x)=e^{\frac{x}{2}}-\frac{x}{4}$, where $e$ is the base of the natural logarithm, if $g(x)=(x+1)f'(x)$ (where $f'(x)$ is the derivative of $f(x)$).

(Ⅰ) Determine the monotonicity of $g(x)$ on $(-1,+\infty)$;

(Ⅱ) If $F(x)=\ln(x+1)-af(x)+4$ has no zeros, determine the range of values for the positive number $a$.

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