
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 a trapezoid \(ABCD\) with bases \(AD = 3\) and \(BC = 18\). Point \(M\) is located on the diagonal \(AC\), with the ratio \(AM : MC = 1 : 2\). A line passing through point \(M\) parallel to the bases of the trapezoid intersects the diagonal \(BD\) at point \(N\). Find the length of \(MN\).

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