
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 all pairs  $(x,y)$  of real numbers that satisfy the system \begin{align*} x \cdot \sqrt{1-y^2} &=\frac14 \left(\sqrt3+1 \right),
 y \cdot \sqrt{1-x^2} &= \frac14 \left( \sqrt3 -1 \right).
\end{align*}

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