
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 a city where Dan, Eva, and Fiona live can be represented by a Cartesian plane. Dan is located at $(10, -30)$ and Eva is at $(-2, 20)$. They agree to meet at the closest point that is equidistant from their current locations, then walk 3 units to the right, and from there, walk directly upwards together to reach Fiona, who is located at $(9, 10)$. How many units upward do Dan and Eva walk together from their shifted position to get to Fiona?

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