
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 \(y_1, y_2, \ldots, y_{50}\) be real numbers such that \(y_1 + y_2 + \ldots + y_{50} = 2\) and
\[
\frac{y_1}{2 - y_1} + \frac{y_2}{2 - y_2} + \ldots + \frac{y_{50}}{2 - y_{50}} = 2.
\]
Find
\[
\frac{y_1^2}{2 - y_1} + \frac{y_2^2}{2 - y_2} + \ldots + \frac{y_{50}^2}{2 - y_{50}}.
\]

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