
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
Elective 4-2: Matrix and Transformation:  
Given the curve $C: x^{2}+y^{2}=1$, first apply the transformation corresponding to matrix $A= \begin{bmatrix} 1 & 0 \\ 0 & 2\end{bmatrix}$, then apply the transformation corresponding to matrix $B= \begin{bmatrix} 0 & b \\ 1 & 0\end{bmatrix}$, resulting in the curve $C: \frac {x^{2}}{4}+y^{2}=1$. Find the value of the real number $b$.

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