
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 $f(x) = \ln x + \frac{ax}{x+1}$ (where $a \in \mathbb{R}$),
(1) If the function $f(x)$ is monotonically increasing on the interval $(0, 4)$, find the range of values for $a$;
(2) If the graph of the function $y = f(x)$ is tangent to the line $y = 2x$, find the value of $a$.

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