
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 20 lattice points arranged in a 5x4 grid, each one unit apart. 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<5; ++i) {
for (int j=0; j<4; ++j) {
dot((i,j));
};}
label("$A$",(0,3),W);
label("$B$",(4,0),E);
label("$D$",(1,0),S);
label("$E$",(2.5,1.5),S);
dot((2.5,1.5));
label("$C$",(3,3),N);
draw((0,3)--(4,0),linewidth(0.7));
draw((1,0)--(3,3),linewidth(0.7));
[/asy]

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