
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 $JKLM$, side $JL$ measures $8$ units and side $LM$ measures $4$ units. Points $P$ and $Q$ are on side $JM$ such that segment $JP$ measures $2$ units and segment $QM$ measures $1$ unit. Lines $LP$ and $KQ$ intersect at $R$. What is the area of triangle $LRK$?
```markdown
[asy]
draw((0,0)--(8,0)--(8,4)--(0,4)--cycle);
draw((0,0)--(2.5,4)--(7,4)--(0,0)--cycle); 
dot((0,0));
dot((8,0));
dot((8,4));
dot((0,4));
dot((2.5,4));
dot((7,4));
label("L",(0,0),SW);
label("K",(8,0),SE);
label("M",(8,4),NE);
label("J",(0,4),NW);
label("R",(3,2),N);
label("P",(2.5,4),N);
label("Q",(7,4),N);
label("8",(4,0),S);
label("2",(1.25,4),N);
label("1",(7.5,4),N);
label("4",(8,2),E);
[/asy]
```

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