
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
Determine for which real values of \( m \) the simultaneous equations 
\[
\begin{align*}
y &= mx + z + 2, \\
y &= (3m - 2)x + z + 5
\end{align*}
\]
are satisfied by at least one triplet of real numbers \( (x,y,z) \).
**A)** all \( m \)  
**B)** all \( m \neq 0 \)  
**C)** all \( m \neq 1/2 \)  
**D)** all \( m \neq 1 \)  
**E)** no values of \( m \)

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