
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 $x,$ $y,$ $z$ be integers such that
\[\mathbf{B} = \frac{1}{7} \begin{pmatrix} -5 & x \\ y & z \end{pmatrix}\]and $\mathbf{B}^2 = \mathbf{I}.$  Find the largest possible value of $x + y + z.$

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