
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 a sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$. The sequence satisfies $a\_1=1$, $2a_{n+1}=a\_n$. If the inequality $x^{2}+tx+1 > S_{n}$ holds true for all $n \in \mathbb{N}^*$ when $t \in [-1, 1]$, determine the range of values for the real number $x$.

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