
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 real numbers \( x, y \) and \( z \) satisfy both of the equations below:

\[
\begin{aligned}
& 4x + 7y + z = 11 \\
& 3x + y + 5z = 15
\end{aligned}
\]

Given that \( x + y + z = \frac{p}{q} \) where \( p \) and \( q \) are positive integers and the fraction \( \frac{p}{q} \) is in lowest terms, what is the value of \( p - q \)?

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