
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 $p$: There exists $x \in \mathbb{R}$ such that $mx^2 - mx + 1 < 0$ holds, and $q$: The curve of the equation $\frac{x^2}{m-1} + \frac{y^2}{3-m} = 1$ is a hyperbola. If the proposition $p \land q$ is false and the proposition $p \lor q$ is true, find the range of the real number $m$.

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