
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, $D$ and $E$ are the midpoints of $\overline{AB}$ and $\overline{BC}$ respectively, and $F$ is the midpoint of $\overline{CD}$. Find the sum of the slope and $y$-intercept of the line passing through the points $A$ and $F$. In the coordinate system, $A$ is at $(0,8)$, $B$ at $(0,0)$, $C$ at $(10,0)$, and $D$ and $E$ coordinates to be determined. [Insert diagram similar to original with specified adjustments]
- Diagram not inserted: Assume standard x-y plane visualization with given coordinates and definitions.

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