
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 $x_1,$ $x_2,$ $x_3$ be positive real numbers such that $x_1 + 3x_2 + 5x_3 = 100.$  Find the smallest possible value of
\[ x_1^2 + x_2^2 + x_3^2. \]

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