
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
The diameter divides a circle into two parts. In one of these parts, a smaller circle is inscribed so that it touches the larger circle at point \( M \) and the diameter at point \( K \). The ray \( MK \) intersects the larger circle a second time at point \( N \). Find the length of \( MN \), given that the sum of the distances from point \( M \) to the ends of the diameter is 6.

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