
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 $PQRS$, points $L$ and $M$ trisect $\overline{PQ}$, and points $N$ and $O$ trisect $\overline{RS}$. In addition, $PR = PM = 3$. Calculate the area of quadrilateral $UVWX$ formed in a similar manner to $WXYZ$.

[asy]
unitsize(1cm);
pair P,L,M,Q,N,O,R,S,U,V,W,X;
P=(0,0);
L=(1,0);
M=(2,0);
Q=(3,0);
N=(2,3);
O=(1,3);
R=(0,3);
S=(3,3);
U=(1.5,2.25);
V=(2,1.5);
W=(1.5,0.75);
X=(1,1.5);
draw(P--Q--S--R--cycle,linewidth(0.7));
draw(R--M,linewidth(0.7));
draw(O--Q,linewidth(0.7));
draw(S--L,linewidth(0.7));
draw(P--N,linewidth(0.7));
label("$P$",P,SW);
label("$L$",L,S);
label("$M$",M,S);
label("$Q$",Q,SE);
label("$R$",R,NW);
label("$S$",S,NE);
label("$N$",N,N);
label("$O$",O,N);
label("$U$",U,N);
label("$V$",V,E);
label("$W$",W,S);
label("$X$",X,W);
[/asy]

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