
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
Find the values of $z$ which satisfy the equations $3x^2 + 4x + 6z + 2 = 0$ and $x - 2z + 1 = 0$.
A) $12z^2 + 2z + 1 = 0$
B) $12z^2 + 12z + 1 = 0$
C) $12z^2 + 3z + 4 = 0$
D) $z^2 - 4z + 16 = 0$

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