
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
The integers \( x, y, z \), and \( p \) satisfy the equation \( x^2 + xz - xy - yz = -p \). Given that \( p \) is prime, what is the value of \( |y+z| \) in terms of \( p \) ? Your answer should refer to the variable \( p \) so that it works for every prime number \( p \).

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