
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 a circle C that passes through the points (1, 2) and (2, 1), and its center is on the line $x+y-4=0$.
(Ⅰ) Find the equation of circle C;
(Ⅱ) If a beam of light $l$ is emitted from point A(-3, 3) and hits the x-axis, then is reflected onto circle C, and if the reflection point is M(a, 0), find the range of the real number $a$.

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