
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 park where Alex, Casey, and Jordan are jogging can be represented by the Cartesian plane. Alex is located at $(3, -15)$ and Casey is located at $(-2, 18)$. They agree to meet at the closest point that is equidistant from their current locations and then jog horizontally together to get to Jordan's location at $\left(-\frac{1}{2}, 5\right)$. How many units horizontally do Alex and Casey jog together to get to Jordan?

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