
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 $f(x)=\ln x+ \frac{ax}{x+1} (a\in\mathbb{R})$.

(I) Find the range of values for $a$ such that the function $f(x)$ is monotonically increasing in the interval $(0,4)$.

(II) Find the value of $a$ if the graph of the function $y=f(x)$ is tangent to the line $y=2x$.

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