
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
Let $x_1, x_2, \ldots , x_n$ be a sequence of integers such that
(i) $-2 \le x_i \le 3$ for $i = 1,2, \ldots n$
(ii) $x_1 + \cdots + x_n = 22$; and
(iii) $x_1^2 + \cdots + x_n^2 = 108$.
Let $m$ and $M$ be the minimal and maximal possible values of $x_1^3 + \cdots + x_n^3$, respectively. What is the value of $\frac{M}{m}$?
A) 3
B) 4
C) 5
D) 6

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