
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 lives at the point $(10, -15)$, Barbara lives at $(0, 20)$, and Charlie is at $(5, 12)$. They decide first to meet at a point equidistant from both their starting locations before going to Charlie. Calculate how many units they need to walk vertically from their meeting point to reach Charlie.

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