
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
Let the matrix $M= \begin{pmatrix} 1 & a \\ b & 1 \end{pmatrix}$.

(I) If $a=2$ and $b=3$, find the inverse matrix $M^{-1}$ of matrix $M$;  
(II) If the curve $C: x^2+4xy+2y^2=1$ is transformed into the curve $C′: x^2-2y^2=1$ under the action of matrix $M$, find the value of $a+b$.

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