
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 35 lattice points, arranged in a 7x5 grid, each one unit apart. Segment $AB$ meets segment $CD$ at point $E$. $A$ is at position (0,4), $B$ is at position (6,0), $C$ is at position (3,3), and $D$ is at position (5,0). Each unit corresponds to one segment length between adjacent points. Find the length of segment $AE$.

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