
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 $f(x) = \ln x - ax$, where $a \in \mathbb{R}$.
(1) If the line $y = 3x - 1$ is a tangent line to the graph of the function $f(x)$, find the value of the real number $a$.
(2) If the maximum value of the function $f(x)$ on the interval $[1, e^2]$ is $1 - ae$ (where $e$ is the base of the natural logarithm), find the value of the real number $a$.

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