
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 coordinate grid with 35 lattice points, where each is one unit apart from its nearest neighbors. Line segment $\overline{AB}$ meets line segment $\overline{CD}$ at point $E$. Given that $A$ is at $(0,4)$, $B$ is at $(7,0)$, $C$ is at $(3,0)$, and $D$ is at $(5,3)$, find the length of segment $\overline{AE}$.

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