
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 $f(x)=\frac{a+\ln x}{x}$ where $a\in\mathbb{R}$:

1. If $a=4$, find the equation of the tangent line to the curve $f(x)$ at the point $(1,4)$.
2. If the graph of the function $f(x)$ intersects with the graph of the function $g(x)=1$ in the interval $(0, e^2]$, find the range of values for the real number $a$.

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