
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 $p$: $\frac{1}{2}{x}^{2}-tx+\frac{1}{2}>0$ holds true for all $x\in R$, and $q$: the inequality ${t}^{2}-(a-1)t-a<0 (a\in R)$ is satisfied.

(1) If $p$ is true, find the set of values for real number $t$.

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

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