
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 decreasing function $f(x)=x^{2}-2tx+1$ on the interval $(-\infty,1]$ and for any $x_{1}$, $x_{2} \in [0,t+1]$, it always holds that $|f(x_{1})-f(x_{2})| \leqslant 2$, determine the range of the real number $t$.

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