
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 illustrates 32 lattice points set in an 8x4 grid, each one unit apart from its neighbors vertically and horizontally. Segment $AB$ connects points (0,3) and (7,0). Segment $CD$ connects points (3,0) to (6,3). Find the length of segment $AE$, where $E$ is the intersection of segments $AB$ and $CD$.

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