
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 $f(x) = \ln x$ and $g(x) = \frac{1}{3}x^3 + \frac{1}{2}x^2 + mx + n$, the line $l$ is tangent to the graphs of both functions $f(x)$ and $g(x)$ at the point $(1,0)$.
(1) Find the equation of the line $l$ and the explicit formula for $g(x)$;
(2) If $h(x) = f(x) - g'(x)$ (where $g'(x)$ is the derivative of $g(x)$), find the maximum value of the function $h(x)$.

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