
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, triangle $ABC$ has vertices at points $A(0,8)$, $B(0,0)$, and $C(10,0)$. $D$ and $E$ are the midpoints of $\overline{AB}$ and $\overline{BC}$ respectively. Determine the sum of the $x$ and $y$ coordinates of $F$, the point of intersection of $\overline{AE}$ and $\overline{CD}$. Label points as follows:
- $A(0,8)$ 
- $B(0,0)$
- $C(10,0)$
- $D(0,4)$ (midpoint of $AB$)
- $E(5,0)$ (midpoint of $BC$)
- $F$ (intersection of $\overline{AE}$ and $\overline{CD}$)

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