
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 function $f(x)$ defined on $\mathbb{R}$ such that for any ${x}_{1}, {x}_{2} ({x}_{1} \neq {x}_{2})$, the inequality $\frac{f({x}_{1}) - f({x}_{2})}{{x}_{1} - {x}_{2}} < 0$ holds. The graph of the function $y = f(x - 1)$ is symmetric about the center $(1, 0)$. For $2 \leq s \leq 4$, there always exists a $t$ such that the inequality $f({s}^{2} - 2s) \leq -f(2t - {t}^{2})$ holds. Find the range of possible values for $t$.

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