
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 p: The equation $x^2 + 2mx + (m+2) = 0$ has two distinct positive roots; q: The equation $\frac{x^2}{m+3} - \frac{y^2}{2m-1} = 1$ represents a hyperbola with foci on the y-axis.  
(1) If q is a true statement, determine the range of the real number m;  
(2) If "p or q" is true, and "p and q" is false, determine the range of the real number m.

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