
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 the equation of circle C: $x^2+y^2-2x-4y+m=0$.  
(1) Find the range of values for $m$;  
(2) When $m=4$, find the length of the chord MN cut by the line $l: x+2y-4=0$ on circle C.

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