
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 $f(x)=\ln \left( ax+\frac{1}{2} \right)+\frac{2}{2x+1}$.

(I) If $a > 0$, and the function $f(x)$ is monotonically increasing on $(0,+\infty)$, find the range of values for the real number $a$.

(II) Does there exist a real number $a$ such that the minimum value of the function $f(x)$ on $(0,+\infty)$ is $1$? If so, find the value of $a$; if not, explain why.

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