
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 $\frac{x^2}{m+1} + \frac{y^2}{3-m} = 1$ represents an ellipse with foci on the $y$-axis, and proposition $q$: The equation in terms of $x$, $x^2 + 2mx + 2m + 3 = 0$, has no real roots. If "$p \land q$" is a false proposition and "$p \lor q$" is a true proposition, find the range of the real number $m$.

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