
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
Suppose \(x\) and \(y\) are non-zero integers satisfying the conditions:
\[|x| - y = 5 \quad \text{and} \quad |x|y + x^2 = 6.\]
Find the integer nearest to \(x + y\).
A) -1 
B) 0 
C) 1  
D) 2 
E) 3

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