
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 a constant $a > 0$, consider the function $f(x) = \ln(1 + ax) - \dfrac{2x}{x + 2}$.
$(1)$ Discuss the monotonicity of $f(x)$ on the interval $(0, +\infty)$.
$(2)$ If $f(x)$ has two extrema $x_{1}$ and $x_{2}$ such that $f(x_{1}) + f(x_{2}) > 0$, find the range of values for $a$.

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