
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 \( y_1, y_2, y_3 \) be positive real numbers such that \( 3y_1 + 2y_2 + y_3 = 90 \). Find the smallest possible value of 
\[ y_1^2 + 4y_2^2 + 9y_3^2. \]

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