
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
Let the function $f(x) = \frac{\ln x}{x^2}$.
(1) Find the maximum value of $f(x)$;
(2) If the equation $f(x) - \frac{a}{2e} = 0$ ($a \in \mathbb{R}^+$) has a unique solution, then the equation $g(x) = txf'(x) + \frac{ax^2 - 2tx - t}{x^2} = 0$ also has a unique solution. Find the value of the positive real number $t$.

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