
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 that the real numbers \( x \) and \( y \) satisfy the equations
\[
x^3 + y^3 = 26 \quad \text{and} \quad xy(x+y) = -6,
\]
find the value of \( |x - y| \).

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