
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 $y=f(x)=\frac{\ln x}{x}$.
(1) Find the equation of the tangent line to the graph of the function $y=f(x)$ at $x=\frac{1}{e}$;
(2) Find the maximum value of $y=f(x)$;
(3) Let $a > 0$, find the minimum value of the function $F(x)=af(x)$ on the interval $[a,2a]$.

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