
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
\[
\left\{
\begin{array}{l}
2 - \log_{2} y = 2 \log_{2} (x+y) \\
\log_{2} (x+y) + \log_{2} \left(x^{2} - x y + y^{2} \right) = 1
\end{array}
\right.
\]

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