
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 following system of equations:

$$
\begin{aligned}
& \frac{1}{x}+\frac{1}{2 y}=\left(x^{2}+3 y^{2}\right)\left(3 x^{2}+y^{2}\right) \\
& \frac{1}{x}-\frac{1}{2 y}=2\left(y^{4}-x^{4}\right)
\end{aligned}
$$

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