
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
Given real numbers \( x \) and \( y \) satisfying \( x^2 + y^2 = 1 \), let the maximum and minimum values of \( x^4 + xy + y^4 \) be denoted as \( S_{\text{max}} \) and \( S_{\text{min}} \) respectively. Calculate \( S_{\text{max}} + S_{\text{min}} \).

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