
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 $f(x)=x^2-2tx+1$ which is decreasing on $(-\infty,1]$, and for any $x_1, x_2 \in [0,t+1]$, it always satisfies $|f(x_1)-f(x_2)|\leqslant 2$. Find the range of the real number $t$.

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