
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
The matrices
\[\begin{pmatrix} x & 2 & y \\ 3 & 4 & 5 \\ z & 6 & w \end{pmatrix} \quad \text{and} \quad \begin{pmatrix} -7 & p & -13 \\ q & -15 & r \\ 3 & s & 6 \end{pmatrix}\] are inverses. Find \(x + y + z + w + p + q + r + s.\)

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