
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 the proposition $p$: "The eccentricity $e$ of the hyperbola $\frac{x^2}{3} - \frac{y^2}{m} = 1$ belongs to the interval $(\sqrt{2}, +\infty)$", and the proposition $q$: "The equation $\frac{2x^2}{m} + \frac{y^2}{m-2} = 1$ represents an ellipse with foci on the $x$-axis". If the proposition "$p \land q$" is true, find the range of the real number $m$.

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