
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
Amerigo Vespucci has expanded his map of America on the complex plane, where the coordinates of the cities remain proportionally similar but scaled. Now, Los Angeles is at $0$, New York is at $3900i$, and Nashville is at $1170 + 1560i$. Additionally, a new city, Miami, is located at $1950 + 780i$ on this map. Calculate the distance from Nashville to Miami.

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