
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
A map of the town where Annie, Barbara, and David live can be represented by the Cartesian plane. Annie is located at $(6,-20)$, Barbara is at $(1, 14)$, and David is at $(0, -6)$. They agree to meet at the closest point that is equidistant from all their locations before walking upwards together to get to Charlie's location at $\left(\frac{7}{2}, 2\right)$. How many units upward do Annie, Barbara, and David walk together to get to Charlie?

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