
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
The diagram shows 36 lattice points forming a 6x6 grid, each point one unit from its nearest neighbors. Line segment $AB$ meets line segment $CD$ at point $E$. Find the length of segment $AE$.

[asy]
unitsize(0.8cm);
for (int i=0; i<6; ++i) {
for (int j=0; j<6; ++j) {
dot((i,j));
};}
label("$A$",(0,5),W);
label("$B$",(5,0),E);
label("$D$",(1,0),S);
label("$E$",(2.5,2.5),S);
dot((2.5,2.5));
label("$C$",(3,4),N);
draw((0,5)--(5,0),linewidth(0.7));
draw((1,0)--(3,4),linewidth(0.7));
[/asy]

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