
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$, $ x$, $ y$, and $ z$ be real numbers that satisfy the three equations
\begin{align*}
  17x +  by +  cz &= 0 \\
   ax + 29y +  cz &= 0 \\
   ax +  by + 37z &= 0.
\end{align*}
Suppose that $ a \ne 17$ and $ x \ne 0$.  What is the value of
\[ \frac{a}{a - 17} + \frac{b}{b - 29} + \frac{c}{c - 37} \, ?\]

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