
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: $(x-1)^2+(y-2)^2=4$.  
(1) Find the length of the chord cut by the line $2x-y+4=0$ on circle C;  
(2) Find the equation of the tangent line to circle C that passes through point M(3, 1).

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