
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:

\[
\begin{cases} 
x + 3y + 14 \leq 0, \\ 
x^4 + 2x^2y^2 + y^4 + 64 - 20x^2 - 20y^2 = 8xy.
\end{cases}
\]

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