
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 diagram, let $A$ be positioned at $(4,10)$ and $B$ at the origin $(0,0)$. $C$ is located at $(12,0)$. Let $D$ and $E$ still be midpoints of $\overline{AB}$ and $\overline{BC}$ respectively. Find the difference between the slopes of the lines passing through $A$ and $D$, and $C$ and $E$.

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