
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 the given 36 lattice points arranged in a 6x6 grid where each point is one unit from its nearest neighbors, segment $AB$ meets segment $CD$ at point $E$. Points are as follows: $A(0,5)$, $B(5,0)$, $D(1,0)$, and $C(5,3)$. Determine the length of segment $AE$.

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