
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. Determine the sum of the $x$ and $y$ coordinates of $F$, the point of intersection of $\overline{AE}$ and $\overline{CD}$. Given:
- Point $A$ is at $(0,8)$
- Point $B$ is at $(0,0)$
- Point $C$ is at $(10,0)$ [asy]
size(200); defaultpen(linewidth(.7pt)+fontsize(10pt));
pair A, B, C, D, E, F;
A=(0,8);
B=(0,0);
C=(10,0);
D=(0,4);
E=(5,0);
F=(10/3,16/3);
draw(E--A--C--D);
draw(D--B, dashed);
draw((-1,0)--(12,0), EndArrow);
draw((0,-1)--(0,9), EndArrow);
label("$A(0,8)$", A, NW);
label("$B(0,0)$", B, SW);
label("$C(10,0)$", C, SE);
label("$D$", D, W);
label("$E$", E, S);
label("$F$", F, NE);
label("$x$", (12,0), dir(0));
label("$y$", (0,9), dir(90));
[/asy]

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