
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 $f(x) = -(x+2)(x-m)$ (where $m > -2$), and $g(x) = 2^x - 2$.
(1) Let proposition $p$: $f(x) \geq 0$, and proposition $q$: $g(x) < 0$. If $p$ is a sufficient but not necessary condition for $q$, find the range of $m$.
(2) Let proposition $p$: $\forall x \in \mathbb{R}, f(x) < 0$ or $g(x) < 0$; proposition $q$: $\exists x \in (-1, 0). f(x) \cdot g(x) < 0$. If $p \land q$ is true, find the range of $m$.

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