
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
If the solution set of the inequality $x^2 + ax - c < 0$ with respect to $x$ is $\{x \mid -2 < x < 1\}$, and for any $t \in [1, 2]$, the function $f(x) = ax^3 + (m + \frac{1}{2})x^2 - cx$ is not monotonic in the interval $(t, 3)$, find the range of values for the real number $m$.

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