
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
$PQRS$ is a rectangle with an area of 20 square units. Inside $PQRS$, there is a trapezoid $TUVS$ formed by subdividing the rectangle using various cut segments. Point $T$ is on $PS$ 2 units from $P$, point $U$ is on $QR$ 2 units from $Q$, and point $V$ is directly opposite $T$ on $RS$ such that $VT$ is parallel to $PS$. Find the area of the trapezoid $TUVS$?

[asy]
size(6cm,6cm);

draw((0,0)--(5,0)--(5,4)--(0,4)--cycle);
draw((2,0)--(3,4));

label("$P$",(0,0),SW);
label("$Q$",(5,0),SE);
label("$R$",(5,4),NE);
label("$S$",(0,4),NW);
label("$T$",(2,0),S);
label("$U$",(3,4),N);
label("$V$",(5,4),N);

[/asy]

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