
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 $p$: For all $x \in [0, 1]$, the inequality $2x-2 \ge m^2-3m$ always holds; proposition $q$: There exists $x \in [-1, 1]$ such that $x^2-m \ge 0$ holds. If the proposition $p \lor q$ is true, and $p \land q$ is false, then the range of the real number $m$ is \_\_\_\_\_.

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