
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
For some value of $k$, consider the system:
\begin{align*}
x + ky + 3z &= 0, \\
3x + ky - 2z &= 0, \\
x + 6y - 5z &= 0
\end{align*}
This system has a nontrivial solution where $x, y, z$ are all non-zero. Find $\frac{yz}{x^2}$.

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