
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 \(\mathbf{N} = \begin{pmatrix} -1 & 4 \\ -6 & 3 \end{pmatrix}\). Determine scalars \(r\) and \(s\) such that
\[
\mathbf{N}^2 = r \mathbf{N} + s \mathbf{I}.
\]
where \(\mathbf{I}\) is the identity matrix.

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