
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
Triangle $PQR$ is found within a rectangle that measures 3 units by 6 units. Vertex $P$ is located at (0,2), vertex $Q$ at (3,0), and vertex $R$ at (1,6). What is the area of triangle $PQR$ in square units?

[asy]
fill((0,2)--(3,0)--(1,6)--cycle,lightgray);

// Draw the mesh
for(int i=1; i < 6; ++i) {
    draw((0,i)--(3,i),dashed);
}
for(int k=1; k < 3; ++k) {
    draw((k,0)--(k,6),dashed);
}

// Draw rectangle and triangle
draw((0,0)--(3,0)--(3,6)--(0,6)--cycle);
draw((0,2)--(3,0)--(1,6)--cycle);

// Label points
label("$P$",(0,2),W);
label("$Q$",(3,0),SE);
label("$R$",(1,6),N);
[/asy]

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