
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
If the matrix $\begin{pmatrix}3x & 2\\ x & 2x\end{pmatrix}$ has the determinant $ad-bc$, determine the values of $x$ such that the determinant equals 4.
A) $x = -\frac{2}{3}$ and $x = 1$  
B) $x = \frac{2}{3}$ and $x = 1$  
C) $x = -2$ and $x = 1$  
D) $x = 2$ and $x = -1$  
E) No solution

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