
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
\[\bold{B} = \begin{pmatrix} 1 & 0 & 3 \\ 0 & 1 & 0 \\ 3 & 0 & 1 \end{pmatrix}.\]
Determine the constants $p$, $q$, and $r$ so that
\[\bold{B}^3 + p \bold{B}^2 + q \bold{B} + r \bold{I} = \bold{0},\]where $\bold{I}$ and $\bold{0}$ are the $3 \times 3$ identity matrix and zero matrix, respectively. Enter the ordered triple $(p, q, r)$.

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