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

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