
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
Annie, Barbara, and Charlie live in a town depicted by a Cartesian plane. Annie is located at $(8, -15)$ and Barbara is at $(2, 10)$. They have decided to meet at the closest point that is equidistant from both their locations, and then proceed straight up together to Charlie's new location at $(5, 3)$. What is the total distance they must walk upwards to reach Charlie?

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