
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 $f(x)=\ln x+ \frac{7a}{x}$, where $a\in R$.
(1) If the function $y=f(x)$ has exactly one zero in its domain, find the range of values for the real number $a$.
(2) If the minimum value of the function $y=f(x)$ on $[e,e^{2}]$ is $3$, find the value of the real number $a$. ($e$ is the base of the natural logarithm)

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