
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
Consider the system of equations

\[
8x - 6y = c,
\]
\[
12y - 18x = d.
\]

If this system has a solution \((x, y)\) where both \(x\) and \(y\) are nonzero, find the value of \(\frac{c}{d}\), assuming \(d\) is nonzero.

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