
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 \(x_1 + 3x_2 + 4x_3 = 72\). Additionally, \(x_1 = 3x_2\). Find the smallest possible value of
\[
x_1^2 + x_2^2 + x_3^2.
\]

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