
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 $y_1, y_2, \dots, y_50$ be real numbers such that $y_1 + y_2 + \dots + y_50 = 2$ and
\[
\frac{y_1^2}{1 - y_1} + \frac{y_2^2}{1 - y_2} + \dots + \frac{y_{50}^2}{1 - y_{50}} = 2.
\]
Find
\[
\frac{y_1^3}{1 - y_1} + \frac{y_2^3}{1 - y_2} + \dots + \frac{y_{50}^3}{1 - y_{50}}.
\]

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