
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 that line $x - 2y + 3 = 0$ and parabola $y^2 = mx (m \neq 0)$ have no intersections, and statement $q$: the equation $\frac{x^2}{5 - 2m} + \frac{y^2}{m} = 1$ represents a hyperbola, find the range of real number $m$ if $p \vee q$ is true and $p \wedge q$ is false.

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