
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 rectangle $LMNO$, points $Q$ and $R$ bisect $\overline{LN}$, and points $S$ and $T$ bisect $\overline{MO}$. If $\overline{LN}=12$ and $\overline{LM}=8$, find the area of the quadrilateral $WXYZ$ formed by connecting midpoints $Q$ and $S$ to points $B$ and $D$, which are the midpoints of segments $\overline{MS}$ and $\overline{NT}$ respectively.

[asy]
unitsize(1cm);
pair L, M, N, O, Q, R, S, T, W, X, Y, Z;
L=(0,0);
M=(0,8);
N=(12,0);
O=(12,8);
Q=(3,0); // midpoint of LN first half
R=(9,0); // midpoint of LN second half
S=(12,2); // midpoint of MO first half
T=(12,6); // midpoint of MO second half
W=(6,1); //Midpoint of QS
X=(6,0); // Midpoint of QR
Y=(10.5,4); // Midpoint of TD
Z=(10.5,2); // Midpoint of TS
draw(L--M--O--N--cycle,linewidth(0.7));
draw(Q--S);
draw(R--T);
draw(S--M);
draw(N--T);
label("$L$",L,S);
label("$M$",M,N);
label("$N$",N,S);
label("$O$",O,N);
label("$Q$",Q,S);
label("$R$",R,S);
label("$S$",S,E);
label("$T$",T,E);
label("$W$",W,N);
label("$X$",X,S);
label("$Y$",Y,E);
label("$Z$",Z,W);
draw(M--S);
draw(N--T);
draw(W--X--Y--Z--cycle);
[/asy]

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