
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
Regular dodecagon \( ABCDEFGHIJKL \) is divided into twelve smaller equilateral triangles by joining the center \( M \) with all other vertices. By connecting every third vertex (starting from \( A \)), we obtain a larger equilateral triangle \( ADGJ \), also highlighted in boldface in the diagram below. Compute the ratio of the area of one of the smaller triangles, such as \( \triangle ABM \), to the area of triangle \( \triangle ADGJ \).
[This problem requires visualization, but assumes a standard, symmetrically divided dodecagon centered at \( M \) with evenly spaced vertices on a circle.]

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