
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
The side length of a regular hexagon is 12 cm. Calculate the area of the shaded trapezoidal region formed by connecting the midpoints of alternate sides of the hexagon. Express your answer in simplest radical form.

[asy]
size(100);

pair A,B,C,D,E,F;
A = dir(0); B = dir(60); C = dir(120); D = dir(180); E = dir(240); F = dir(300);
pair M1, M2, M3, M4;
M1 = (A+C)/2; M2= (C+E)/2; M3 = (E+A)/2; M4 = (B+D)/2;
fill(M1--M2--M3--M4--cycle,heavycyan);

draw(A--B--C--D--E--F--A);
[/asy]

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