
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
Let the function $f(x) = x^2 - 2tx + 2$, where $t \in \mathbb{R}$.
1. If $t=1$, find the range of values of the function $f(x)$ in the interval $[0, 4]$.
2. If $t=1$, and for any $x \in [a, a+2]$, $f(x) \leq 5$, find the range of values for the real number $a$.
3. If for any $x_1, x_2 \in [0, 4]$, $|f(x_1) - f(x_2)| \leq 8$, find the range of values for $t$.

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