
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. Given the new coordinates \(A(0,8)\), \(B(0,0)\), and \(C(10,0)\), determine the sum of the \(x\) and \(y\) coordinates of \(G\), the point of intersection of \(\overline{AF}\) and \(\overline{CE}\), where \(F\) is the midpoint of \(\overline{AC}\). 
[asy]
size(180); defaultpen(linewidth(.7pt)+fontsize(10pt));
pair A, B, C, D, E, F, G;
A=(0,8);
B=(0,0);
C=(10,0);
D=(0,4);
E=(5,0);
F=(5,4);
G=(10/3,16/3);
draw(E--A--C--B--D);
draw(F--E);
dot("$A(0,8)$", A, NW);
dot("$B(0,0)$", B, S);
dot("$C(10,0)$", C, S);
dot("$D$", D, W);
dot("$E$", E, S);
dot("$F$", F, N);
dot("$G$", G, NE);
[/asy]

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