
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
Solve the system of equations:
$$
\left\{\begin{array}{l}
\left(1-x^{2}\right) y_{1}=2 x, \\
\left(1-y_{1}^{2}\right) y_{2}=2 y_{1}, \\
\left(1-y_{2}^{2}\right) y_{3}=2 y_{2}, \\
y_{3}=x .
\end{array}\right.
$$

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