
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 $p$, $q$, and $r$ be integers such that:
\[\mathbf{B} = \frac{1}{4} \begin{pmatrix} -1 & p \\ q & r \end{pmatrix}\]
and $\mathbf{B}^2 = \mathbf{I}.$ Find the largest possible value of $p + q + r$.

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