
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
\[\begin{pmatrix} x & 2 & y \\ 3 & 3 & 4 \\ z & 6 & w \end{pmatrix} \quad \text{and} \quad \begin{pmatrix} -6 & j & -12 \\ k & -14 & l \\ 3 & m & 5 \end{pmatrix}\]
are inverses. Find $x + y + z + w + j + k + l + m.$

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