
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 now involves 35 lattice points arranged in a 7x5 grid, each one unit apart. Segment $AB$ meets segment $CD$ at point $E$. Find the length of segment $AE$.

[asy]
unitsize(0.8cm);
for (int i=0; i<7; ++i) {
    for (int j=0; j<5; ++j) {
        dot((i,j));
    };
}
label("$A$", (0, 4), W);
label("$B$", (6, 0), E);
label("$D$", (2, 0), S);
label("$E$", (4, 2), NE);
dot((4, 2));
label("$C$", (6, 4), N);
draw((0, 4)--(6, 0), linewidth(0.7));
draw((2, 0)--(6, 4), linewidth(0.7));
[/asy]

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