
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
A line joins the points $(1,1)$ and $(5,5)$ and divides a square of side length 6, with a corner at the origin $(0,0)$ and another at $(6,0)$. What fraction of the area of the square is below this line? Provide your answer in the simplest fractional form.

[asy]
draw((-1,0)--(7,0),linewidth(1),Arrows);
draw((0,-1)--(0,7),linewidth(1),Arrows);

draw((1,0)--(1,-.25),linewidth(1));
draw((2,0)--(2,-.25),linewidth(1));
draw((3,0)--(3,-.25),linewidth(1));
draw((4,0)--(4,-.25),linewidth(1));
draw((5,0)--(5,-.25),linewidth(1));
draw((6,0)--(6,-.25),linewidth(1));

draw((0,1)--(-.25,1),linewidth(1));
draw((0,2)--(-.25,2),linewidth(1));
draw((0,3)--(-.25,3),linewidth(1));
draw((0,4)--(-.25,4),linewidth(1));
draw((0,5)--(-.25,5),linewidth(1));
draw((0,6)--(-.25,6),linewidth(1));

draw((0,0)--(6,0)--(6,6)--(0,6)--cycle,linewidth(2));

label("$y$",(0,7),N);
label("$x$",(7,0),E);
label("$(0,6)$",(0,6),N);
label("$(6,0)$",(6,0),SE);
[/asy]

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