
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 $PQRS$, $PQ = 8$ and $QR = 4$. Points $T$ and $U$ are on $\overline{RS}$ such that $RT = 2$ and $SU = 3$. Lines $PT$ and $QU$ intersect at $V$. Find the area of $\triangle PVQ$. [asy]
pair P,Q,R,S,V,T,U;
P=(0,0);
Q=(8,0);
R=(8,4);
S=(0,4);
T=(2,4);
U=(6,4);
V=(3.2,6);
draw(P--Q--R--S--cycle,linewidth(0.7));
draw(P--T--V--cycle,linewidth(0.7));
label("$P$",P,SW);
label("$Q$",Q,SE);
label("$R$",R,NE);
label("$S$",S,NW);
label("$T$",T,S);
label("$U$",U,S);
label("$V$",V,N);
label("2",(1,4),N);
label("3",(7,4),N);
label("4",(8,2),E);
label("8",(4,0),S);
[/asy]

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