
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
From the diagram below, find the positive difference in the $x$-coordinates when lines $l$ and $m$ reach $y = 20.$ 
[asy]
import cse5; import olympiad;
size(120);
add(grid(8,8));
draw((0,0)--(8,0),linewidth(1.2));
draw((0,0)--(0,8),linewidth(1.2));
label("$x$",(8,0),E);
label("$y$",(0,8),N);
draw((0,6)--(4,0),Arrows);
draw((0,3)--(6,0),Arrows);
label("$l$",(0,6)--(4,0),NE);
label("$m$",(0,3)--(6,0),NE);
[/asy]

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