
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 $f(x)=ax^{2}+2ax-\ln (x+1)$, where $a\in\mathbb{R}$.
(1) Discuss the monotonicity of $f(x)$;
(2) If $f(x)+e^{-a} > \frac {1}{x+1}$ holds true in the interval $(0,+\infty)$ ($e$ is the base of the natural logarithm), find the range of the real number $a$.

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