
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 $m \in \mathbb{R}$, let proposition $p$: $\forall x \in [0,1]$, $2x-2 \geq m^2 - 3m$, and proposition $q$: $\exists x_0 \in [-1,1]$, $m \leq x_0$.
1. If $p$ is true, find the range of real numbers $m$.
2. If the proposition "$p \land q$" is false and the proposition "$p \lor q$" is true, find the range of real numbers $m$.

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