
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
\[\frac{y_1}{2 - y_1} + \frac{y_2}{2 - y_2} + \dots + \frac{y_{50}}{2 - y_{50}} = 2.\]
Find
\[\frac{y_1^2}{2 - y_1} + \frac{y_2^2}{2 - y_2} + \dots + \frac{y_{50}^2}{2 - y_{50}}.\]

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