
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 rotation transformation matrix A= $$\begin{bmatrix} 0 & -1 \\ 1 & 0\end{bmatrix}$$, if $$\begin{bmatrix} a & b \\ 1 & 2\end{bmatrix}$$•A= $$\begin{bmatrix} 3 & 4 \\ c & d\end{bmatrix}$$, find the value of ad-bc.

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