
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
(The full score of this question is 14 points) Given the function $f(x) = x\ln x$.
(1) Find the extreme values of the function $f(x)$;
(2) Let the function $g(x) = f(x) - (x - 1)$, where $k \in \mathbb{R}$, find the maximum value of the function $g(x)$ on the interval $[1, e]$.

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