
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

\begin{align*}
8x - 6y &= c, \\
10y - 15x &= d.
\end{align*}

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