
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 a coordinate plane, points $A$, $B$, and $C$ have coordinates $(0,8)$, $(0,0)$, and $(10,0)$ respectively. $D$ and $E$ are midpoints of segments $\overline{AB}$ and $\overline{BC}$. Find the sum of the $x$ and $y$ coordinates of point $F$, where lines $\overline{AE}$ and $\overline{CD}$ intersect.

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