
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
Find the smallest integer $n$ such that $(x_1^2 + x_2^2 + ... + x_n^2)^2 \leq n(x_1^4 + x_2^4 + ... + x_n^4)$ holds for all real numbers $x_1, x_2, ..., x_n$ and any integer $n \geq 2$.
- **A)** $1$
- **B)** $2$
- **C)** $3$
- **D)** $4$
- **E)** $5$

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