
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 point $M(3,-1)$, it is rotated $90^{\circ}$ counterclockwise around the origin and then transformed by the matrix $A= \begin{bmatrix} a & 0 \\ 2 & b\\end{bmatrix}$ to obtain point $N (3,5)$. Find the values of $a$ and $b$.

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