
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
Points \( E, F, M \) are located on the sides \( AB, BC, \) and \( AC \) of triangle \( ABC \), respectively. The segment \( AE \) is one third of side \( AB \), the segment \( BF \) is one sixth of side \( BC \), and the segment \( AM \) is two fifths of side \( AC \). Find the ratio of the area of triangle \( EFM \) to the area of triangle \( ABC \).

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