
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
In an $8 \times 5$ grid of lattice points, where each point is one unit away from its nearest neighbors horizontally and vertically, consider the following points: $A(0, 4)$, $B(7, 0)$, $C(5, 3)$, and $D(3, 0)$. Segment $AB$ meets segment $CD$ at $E$. Find the length of segment $AE$.

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