
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
Suppose $3x - 2y - 4z = 0$ and $2x + y - 9z = 0$, for $z \neq 0$. Determine the numerical value of $\frac{x^2 - 2xy}{y^2 + 2z^2}$.
**A)** $-\frac{24}{25}$ 
**B)** $-\frac{6}{7}$
**C)** $\frac{44}{49}$
**D)** $-\frac{38}{49}$
**E)** $\frac{3}{25}$

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