
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
Given the matrix expression evaluation rule, $\begin{pmatrix}a & c\\ d & b\end{pmatrix} = ab - cd$. Determine the value of $x$ that satisfies the equation $\begin{pmatrix}3x & x+1\\ 2x & x+2\end{pmatrix} = 6$.
A) $x = -2 + \sqrt{10}$
B) $x = -2 - \sqrt{10}$
C) $x = 2 + \sqrt{10}$
D) $x = 2 - \sqrt{10}$
E) None of these.

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