
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
Segments \( AB \) and \( CD \), with lengths 3 and 4 respectively, are chords of a circle with radius 5. Points \( M \) and \( N \) are located on these segments such that \( AM:MB = 1:2 \), and \( CN:ND = 1:3 \). Find the minimum and maximum possible lengths of segment \( MN \) given these conditions.

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