
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 $f(x)=\ln x-x^{2}-x$.
- $(1)$ Find the maximum value of the function $f(x)$;
- $(2)$ If the graph of the function $g(x)=af(x)+ax^{2}-3$ $(a\in\mathbb{R})$ has a tangent at the point $(2,g(2))$ that is parallel to the line $x-y=3$, and for any $t\in[1,2]$, the function $h(x)=x^{3}+x^{2}[g'(x)+ \frac {m}{2}]$ is not always monotonic in the interval $(t,4)$, find the range of values for $m$.

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