
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

Determine all pairs \((x, y)\) of real numbers that satisfy the following system of inequalities:

\[ 
\begin{aligned}
x^{4}+8x^{3}y+16x^{2}y^{2}+16 & \leq 8x^{2}+32xy, \\
y^{4}+64x^{2}y^{2}+10y^{2}+25 & \leq 16xy^{3}+80xy.
\end{aligned}
\]

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