
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 circle C: (x-4)²+(y+2)²=5. Let M be the point on the line y=x+2 that is closest to the center of the circle C. Draw a tangent line from point M to the circle C, and let N be the point of tangency. Find the length of the line segment MN.

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