
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 dimensions $6$ units by $3$ units, resulting in an area of $18$ square units. Diagonally from point $R$, a line segment extends, cutting rectangle height into the ratio $2:1$. This line intersects the top side `PQ` at a new point $T$. Determine the area of trapezoid $TQSR$.

[asy]
size(6cm,3cm);

// Draw rectangle PQRS
draw((0,0)--(6,0)--(6,3)--(0,3)--cycle);

// Points S, R on the left
label("$P$",(0,3),NW);
label("$Q$",(6,3),NE);
label("$R$",(6,0),SE);
label("$S$",(0,0),SW);
label("$T$",(2,3),N);

// Draw line PST
draw((6,0)--(2,3));

[/asy]

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