
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 functions, $f(x)=m\ln(x+1)$, $g(x)= \frac{x}{x+1} (x > 1)$.

(1) Discuss the monotonicity of the function $F(x)=f(x)-g(x)$ on $(-1,+\infty)$;

(2) If $y=f(x)$ and $y=g(x)$ have exactly one common tangent line, find the value of the real number $m$.

(Note: This is an optional question. Candidates should choose to answer either question 22 or 23. If more than one is answered, only the first one will be scored.)

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