
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
Let $x$ and $y$ be non-zero real numbers such that:
\[|x| - y = 4 \qquad \text{and} \qquad |x|y - x^3 = 1.\]
Find the integer nearest to $x - y$.
A) -3
B) -1
C) 2
D) 3
E) 4

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