
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 $p: \exists x \in \mathbb{R}, 2x^2 + (m-1)x + \frac{1}{2} \leqslant 0$, and $q$: "The curve $C: \frac{x^2}{m^2} + \frac{y^2}{2m+8} = 1$ represents an ellipse with foci on the $x$-axis", and $s$: "The curve $C: \frac{x^2}{m-t} + \frac{y^2}{m-t-1} = 1$ represents a hyperbola":

$(1)$ If "$p \land q$" is a true proposition, find the range of values for $m$;

$(2)$ If $q$ is a necessary but not sufficient condition for $s$, find the range of values for $t$.

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