
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
Consider a regular hexagon with side length 12 cm. The shaded region is formed by joining midpoints of non-adjacent sides to create a trapezoid. Calculate the area of this shaded region.

[asy]
size(120);
pair A,B,C,D,E,F,M,N,P,Q;
A = dir(0); B = dir(60); C = dir(120); D = dir(180); E = dir(240); F = dir(300);
M = midpoint(A--C);
N = midpoint(D--B);
P = midpoint(E--C);
Q = midpoint(F--A);

fill(M--N--P--Q--cycle,heavycyan);

draw(A--B--C--D--E--F--A);
draw(M--N--P--Q--M);
label("$A$",A,E); label("$B$",B,NE); label("$C$",C,NW); label("$D$",D,W); label("$E$",E,SW); label("$F$",F,SE);
label("$M$",M,N); label("$N$",N,NE); label("$P$",P,W); label("$Q$",Q,E);
[/asy]

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