
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
In the Cartesian coordinate system on the plane xOy, it is known that there is a circle C defined by \((x-a)^2+(y-a+2)^2=1\), and there is a point A at (0, 2). If there exists a point M on circle C such that \(MA^2+MO^2=10\), then the range of values for the real number \(a\) is ______.

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