
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 matrices $M= \begin{bmatrix} 1 & a \\ b & 1\end{bmatrix}$, $N= \begin{bmatrix} c & 2 \\ 0 & d\end{bmatrix}$, if $MN= \begin{bmatrix} 2 & 4 \\ -2 & 0\end{bmatrix}$. Find the values of the real numbers $a$, $b$, $c$, $d$.

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