
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
\[ \bold{B} = \begin{pmatrix} 2 & 3 & 0 \\ 3 & 2 & 3 \\ 0 & 3 & 2 \end{pmatrix} \]
Determine the constants \( p \), \( q \), and \( r \) such 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.

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