
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 function $f(x) = x^2 - 2ax + 5$ where $a > 1$.
1. If the domain and range of $f(x)$ are both $[1,a]$, find the value of the real number $a$.
2. If for any $x_{1}$, $x_{2} \in [1,a+1]$, $|f(x_{1}) - f(x_{2})| \leq 4$, find the range of values for the real number $a$.

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