
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 people are playing a game; one of them thinks of a set of integers (\( x_{1}, x_{2}, \ldots, x_{n} \))—single-digit integers, both positive and negative. The second person is allowed to ask for the value of the sum \( a_{1} x_{1} + \ldots + a_{n} x_{n} \), where \( \left(a_{1} \ldots a_{n}\right) \) is any set of coefficients. What is the minimum number of questions required for the guesser to determine the original set of integers?

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