
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
Anna and Béla play the following game: Anna thinks of a sequence of natural numbers \(\left(a_{1}, a_{2}, a_{3}, a_{4}\right)\). Béla then names a sequence of natural numbers \(\left(b_{1}, b_{2}, b_{3}, b_{4}\right)\). Anna responds with the sum \(a_{1} b_{1} + a_{2} b_{2} + a_{3} b_{3} + a_{4} b_{4}\). After this, Béla can name new sequences. What is the minimum number of sequences Béla needs in order to determine Anna's numbers?

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