
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 $p: \frac{x^2}{m+3} + \frac{y^2}{7m-3} = 1$ represents a hyperbola with foci on the $x$-axis; the proposition $q: f(x) = (5-2m)^x$ is an increasing function. If $p \vee q$ is true and $p \wedge q$ is false, find the range of real numbers for $m$.

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