
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 $ABCD$, $AB=7$ and $BC=4$. Points $J$ and $K$ are on $\overline{CD}$ such that $DJ = 2$ and $KC=3$. Lines $AJ$ and $BK$ intersect at point $L$. Find the area of $\triangle ABL$. Visualize as follows:
[asy]
pair A,B,C,D,L,J,K;
A=(0,0);
B=(7,0);
C=(7,4);
D=(0,4);
J=(2,4);
K=(4,4);
L=(3.5,6);
draw(A--B--C--D--cycle,linewidth(0.7));
draw(A--J--L--B--K--cycle,linewidth(0.7));
label("$A$",A,SW);
label("$B$",B,SE);
label("$C$",C,NE);
label("$D$",D,NW);
label("$J$",J,S);
label("$K$",K,S);
label("$L$",L,N);
label("2",(1,4),N);
label("1",(3,4),N);
label("3",(5.5,4),N);
label("4",(0,2),W);
label("4",(7,2),E);
label("7",(3.5,0),S);
[/asy]

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