
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 xOy, point A is at (0, 3), and line $l$ is defined by $y=2x-4$. Suppose circle C has a radius of 1, and its center lies on line $l$.
(1) If the center of circle C also lies on the line $y=-x+5$, find the equation of circle C;
(2) Under the condition of (1), draw a tangent line from point A to circle C, and find the equation of the tangent line;
(3) If there exists a point M on circle C such that $|MA|=|MO|$, find the range of values for the x-coordinate $a$ of the center of circle C.

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