
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
A solid right prism \(ABCDEFHIJKL\) has a height of 20 units. Its bases are regular hexagons with a side length of 10 units. Points \(M\), \(N\), and \(O\) are located on the edges \(AB\), \(CD\), and \(EF\) respectively, such that \(AM = \frac{1}{3}AB\), \(CN = \frac{1}{4}CD\), and \(EO = \frac{1}{2}EF\). Determine the perimeter of triangle \(MNO\).

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