
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 $\mathbf{N} = \begin{pmatrix} 4 & 0 \\ 2 & -6 \end{pmatrix}$. Find constants $c$ and $d$ so that
\[\mathbf{N}^{-1} = c \mathbf{N} + d \mathbf{I}.\]
Enter the ordered pair $(c,d)$.

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