
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 $f(x)=x^{2}-2ax+5$ $(a > 1)$, if $f(x)$ is a decreasing function in the interval $(-\infty,2]$, and for any $x\_1$, $x\_2\in[1,a+1]$, we always have $|f(x\_1)-f(x\_2)|\leqslant 4$, find the range of values for $a$.

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