
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 that the function $y=f(x)$ is an even function on $\mathbb{R}$ and is decreasing on $(-\infty, 0]$, if the real number $a$ satisfies $f(a) \leq f(2)$, then the range of values for $a$ is; the maximum value of $a^2-2a+2$ is.

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