
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 a map of an imaginary land drawn on the complex plane. The map preserves distances accurately. The city of Alpha corresponds to the origin $0$ on this complex plane, and the city of Omega corresponds to $3900i$. Meanwhile, the city of Beta is located at the point $1170 + 1560i$. Calculate the distance from Beta to Alpha using the complex plane.

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