
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 $f(x)=x^{2}-2ax+5 (a > 1)$.

1. If the domain and range of the function $f(x)$ are both $[1,a]$, find the value of the real number $a$.
2. If $f(x)$ is a decreasing function on the interval $(-∞,2]$, and for any $x_{1}$, $x_{2}∈[1,a+1]$, we always have $|f(x_{1})-f(x_{2})|≤slant 4$, find the range of values for the real number $a$.
3. If $f(x)$ has a zero in the interval $[1,3]$, find the range of values for the real number $a$.

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