
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
Consider a 5x5 grid of lattice points, where each point is one unit from its nearest neighbors. Let $A$ be located at $(0,4)$ and $B$ at $(4,0)$. Let $C$ be at $(1,1)$ and $D$ at $(3,3)$. Segments $AB$ and $CD$ intersect at point $E$. Find the distance $AE$.

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