
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. Triangle $ABC$ is shifted so that point $A$ is now at $(2,8)$, $B$ at $(2,2)$, and $C$ at $(10,2)$. Determine the sum of the $x$ and $y$ coordinates of $F$, the point of intersection of $\overline{AE}$ and $\overline{CD}$.

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