
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
Point \(M\) is located on segment \(AN\), and point \(N\) is located on segment \(BM\). It is known that \(AB = 18\) and \(AM: MN: NB = 1: 2: 3\). Find \(MN\).

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