
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:

$$
\begin{aligned}
x+y & =2a \\
xy\left(x^{2}+y^{2}\right) & =2b^{4} 
\end{aligned}
$$

What are the conditions for obtaining a real solution?

Numerical values: $a=10$, $b^{4}=9375$.

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