
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 proposition $p$: The graph represented by the equation $\frac{x^2}{2-m} + \frac{y^2}{m-1} = 1$ is a hyperbola with foci on the $y$-axis; proposition $q$: The equation $4x^2 + 4(m-2)x + 1 = 0$ has no real roots, and $p \vee q$ is true, $\neg q$ is true, find the range of the real number $m$.

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