
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 \( a \), \( b \), \( c \), \( p \), \( q \), and \( r \) be real numbers that satisfy the three equations
\begin{align*}
  17p +  bq +  cr &= 0 \\
   ap + 29q +  cr &= 0 \\
   ap +  bq + 56r &= 0.
\end{align*}
Suppose that \( a \ne 17 \) and \( p \ne 0 \). What is the value of
\[ \frac{a}{a - 17} + \frac{b}{b - 29} + \frac{c}{c - 56} \, ?\]

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