
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 any $x \in [0, 1]$, the inequality $2x - 2 \geq m^2 - 3m$ always holds; let proposition $q$: there exists $x \in [-1, 1]$ such that $m \leq ax$ holds.  
(1) If $p$ is true, find the range of $m$.  
(2) When $a=1$, if $p \land q$ is false and $p \lor q$ is true, find the range of $m$.

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