
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 $ p$, $ q$, $ r$, $ u$, $ v$, and $ w$ be real numbers satisfying the equations:
\begin{align*}
  17u +  qv +  rw &= 0 \\
   pu + 29v +  rw &= 0 \\
   pu +  qv + 56w &= 0.
\end{align*}
Suppose $ p \ne 17$ and $ u \ne 0$. What is the value of
\[ \frac{p}{p - 17} + \frac{q}{q - 29} + \frac{r}{r - 56} \, ?\]

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