
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 7 by 5 grid context, each one unit apart. Segment $AB$ meets segment $CD$ at point $E$. Find the length of segment $AE$, where:
- $A$ is located at (0,4),
- $B$ is at (6,0),
- $C$ is at (2,1),
- $D$ is at (5,4).

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