
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
Optional Question B, (Elective 4-2: Matrix and Transformation)  
It is known that under the transformation of a second-order matrix $M$, point $A(1,2)$ is transformed into point $A'(7,10)$, and point $B(2,0)$ is transformed into point $B'(2,4)$. Find the inverse matrix $M^{-1}$ of matrix $M$.

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