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

(1) Find the range of values for $m$ if "$p$ and $q$" is a true proposition.

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

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