
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 proposition $P$: The equation $\frac{x^2}{m^2}+\frac{y^2}{2m+8}=1$ represents an ellipse with foci on the $x$-axis, and proposition $Q$: The curve $y=x^2+(2m-3)x+\frac{1}{4}$ intersects the $x$-axis at two distinct points. If the proposition "$P \lor Q$" is true and "$P \land Q$" is false, find the range of the real number $m$.

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