
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 $ABCD$, $AB = 8$ and $BC = 6$. Points $J$ and $K$ are on $\overline{CD}$ such that $DJ = 2$ and $KC = 3$. Lines $AJ$ and $BK$ intersect at $L$. Find the area of $\triangle ABL$. [asy]
pair A,B,C,D,J,K,L;
A=(0,0);
B=(8,0);
C=(8,6);
D=(0,6);
J=(2,6);
K=(5,6);
L=(2.2,8);
draw(A--B--C--D--cycle,linewidth(0.7));
draw(A--J--L--cycle,linewidth(0.7));
label("$A$",A,SW);
label("$B$",B,SE);
label("$C$",C,NE);
label("$D$",D,NW);
label("$J$",J,SE);
label("$K$",K,SW);
label("$L$",L,N);
label("2",(1,6),N);
label("3",(6.5,6),N);
label("6",(0,3),W);
label("6",(8,3),E);
label("8",(4,0),S);
[/asy]

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