
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
In the Kingdom of Mathematics, there was a three-story palace. Seven natural numbers lived in the palace: two on each floor and one in the attic. It is known that on the first floor there was the number 15 with its smaller mysterious neighbor. On the second and third floors, the numbers were equal to the sum and difference of two neighbors living on the floor below. In the attic, there was the number 780, which is equal to the product of two numbers from the third floor. Who was the mysterious neighbor?

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