
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 $x_1,$ $x_2,$ $\dots,$ $x_n$ be nonnegative real numbers such that $x_1 + x_2 + \dots + x_n = 1$ and 
\[x_1^2 + x_2^2 + \dots + x_n^2 \le \frac{1}{50}.\]
Find the smallest possible value of $n.$

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