
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 the values of $x$ for which the matrix $\begin{pmatrix}3x & 4\\ 2x & x\end{pmatrix}$ equals -2.
A) $x = \frac{4 + \sqrt{10}}{3}, \frac{4 - \sqrt{10}}{3}$
B) $x = \frac{4}{3}$
C) $x = \sqrt{10}$
D) $x = -\sqrt{10}$
E) None of these.

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