
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 that the solution to $(x+1)(2-x) \geq 0$ is condition $p$, and the solution to the inequality $x^2+mx-2m^2-3m-1 < 0$ (where $m > -\frac{2}{3}$) is condition $q$:
1. If $p$ is a sufficient but not necessary condition for $q$, find the range of real numbers $m$.
2. If $\neg p$ is a sufficient but not necessary condition for $\neg q$, find the range of real numbers $m$.

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