
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
For any natural number \(n\) and for any set of numbers \(x_{1}, x_{2}, \ldots, x_{n}\) from the interval \([0, 3]\), the equation \(\sum_{i=1}^{n} |x - x_{i}| = a n\) has a solution \(x\) belonging to the interval \([0, 3]\). Indicate which of the following values of \(a\) satisfy this condition:
a) \(a = 0\), b) \(a = \frac{3}{2}\), c) \(a = 2\).

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