
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 that the inverse of matrix A= $$\begin{bmatrix} a & 2 \\ 7 & 3\end{bmatrix}$$ is A<sup>-1</sup>\= $$\begin{bmatrix} b & -2 \\ -7 & a\end{bmatrix}$$, and curve F transforms into curve y=2x under the transformation corresponding to matrix A. Find the equation of curve F.

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