
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, $A$, $B$, and $C$ form a triangle with $A(0,8)$ and $B(0,0)$. Point $C$ has been moved to $(10,0)$. Point $D$ is still the midpoint of $\overline{AB}$, and $E$ is the midpoint of $\overline{BC}$. Point $F$ is located such that it divides segment $AC$ in the ratio 2:1 starting from $A$. Find the sum of the slope and $y$-intercept of the line passing through the points $C$ and $D$.

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