
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 expression $\begin{pmatrix}a & c\\ d & b\end{pmatrix}$ is given by $ab - cd$, find solutions for $x$ in the equation $\begin{pmatrix}3x & 1\\ 2x & 2x+1\end{pmatrix} = 5$.
A) $x = 1$
B) $x = -1$
C) $x = \frac{5}{6}$
D) $x = \pm 1$
E) No solution

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