
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
Given the matrix 
\[
\begin{pmatrix} 
\frac{1}{14} & -\frac{5}{14} & 0 \\ 
-\frac{5}{14} & \frac{24}{14} & 0 \\
0 & 0 & 1
\end{pmatrix}
\]
projects onto a vector \(\begin{pmatrix} x \\ y \\ z \end{pmatrix}\). Find \(\frac{y}{x}\) and \(\frac{z}{x}\).

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