
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 $f(x) = x^2 - 2ax + 2$ where $a \in \mathbb{R}$.
1. If $a=1$, find the maximum value of the function $f(x)$ when $x \in [-1, 2]$.
2. When $x \in [-1, +\infty)$, $f(x) \geq a$ always holds, find the range of values for the real number $a$.

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