
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
If the system of equations
\[
8x - 6y = c, \\
12y - 18x = d,
\]
has a solution \((x, y)\) where \(x\) and \(y\) are both nonzero, find \(\frac{c}{d}\), assuming \(d\) is nonzero.

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