
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
On a Cartesian plane, Nia is located at $(10, -30)$ and Mia is located at $(5, 22)$. They decide to meet at the closest point that is equidistant from their locations and then proceed straight to visit their friend Lia at $(6, 8)$. How many units in total do Nia and Mia travel together straight to get to Lia from their meeting point?

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