
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 propositions $p$ and $q$:
- Proposition $p$: Vector $\overset{⇀}{a} =(1,1,m)$ is parallel to vector $\overset{⇀}{b} =(-1,-1,|m|)$.
- Proposition $q$: The equation $\frac{{x}^{2}}{2m+1}+ \frac{{y}^{2}}{m-3}=1$ represents a hyperbola.
Find the range of valid values for $m$ if both "$\lnot p$" and "$p \lor q$" are true.

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