
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
In the dodecagon \(A B C D E F G H I J K L\), every two adjacent sides are perpendicular, and all sides except sides \(A L\) and \(G F\) are congruent with each other. The sides \(A L\) and \(G F\) are twice as long compared to the other sides. The segments \(B G\) and \(E L\) intersect at point \(M\). Quadrilateral \(A B M J\) has an area of \(1.8 \mathrm{~cm}^{2}\).

Determine the area of quadrilateral \(E F G M\).

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