
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 $\mathbf{B} =\begin{pmatrix}  2 & -3 \\  4 & 5  \end{pmatrix}.$ Determine if there exist scalars $r$ and $s$ such that
\[\mathbf{B}^6 = r \mathbf{B} + s \mathbf{I}.\] If so, find the ordered pair $(r,s)$.

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