
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 a specific value of $k,$ determine the value of $\frac{xz}{y^2}$ for the system
\begin{align*}
x + ky + 4z &= 0, \\
4x + ky - 3z &= 0, \\
3x + 5y - 4z &= 0,
\end{align*}
given that $x,$ $y,$ and $z$ are all nonzero.

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