
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
Two players are playing a game; one of them thinks of a set of integers \( x_{1}, x_{2}, \ldots, x_{n} \), where each \( x_i \) can be a single-digit positive or negative number. The second player is allowed to ask for the sum \( a_{1} x_{1} + \ldots + a_{n} x_{n} \), with any chosen set of coefficients \( \left(a_{1}, \ldots, a_{n}\right) \). What is the minimum number of questions needed for the guesser to find out the thought-of set?

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