
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
Find \( x \) and \( y \) from the system of equations

\[
\frac{x - y \sqrt{x^{2} - y^{2}}}{\sqrt{1 - x^{2} + y^{2}}} = a, \quad \frac{y - x \sqrt{x^{2} - y^{2}}}{\sqrt{1 - x^{2} + y^{2}}} = b
\]

where \( a \) and \( b \) are given numbers.

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