
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 $a$, $b$, $c$, $d$, $w$, $x$, $y$, and $z$ be real numbers satisfying:
\begin{align*}
  17w + bx + cy + dz &= 0 \\
  aw + 29x + cy + dz &= 0 \\
  aw + bx + 37y + dz &= 0 \\
  aw + bx + cy + 53z &= 0.
\end{align*}
Suppose that $a \neq 17$, $b \neq 29$, $c \neq 37$, and $w$, $x$, $y$ do not all equal zero. Determine the value of
\[
\frac{a}{a-17} + \frac{b}{b-29} + \frac{c}{c-37} + \frac{d}{d-53}.
\]

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