
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: $$\frac{x^2}{m+2} - \frac{y^2}{m-3} = 1$$ represents a hyperbola; and the proposition q: The equation $mx^2 + (m+3)x + 4=0$ has no positive real roots. If $p \vee q$ is a true proposition and $p \wedge q$ is a false proposition, determine the range of the real number $m$.

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