
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
If \( x \) and \( y \) are real numbers such that \( x + y = 4 \) and \( xy = -2 \), evaluate the value of \( x + \frac{x^3}{y^2} + \frac{y^3}{x^2} + y \).

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