
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
Given are two 4x4 matrices
\[\begin{pmatrix} a & 1 & b & 2 \\ 2 & 3 & 4 & 3 \\ c & 5 & d & 3 \\ 2 & 4 & 1 & e \end{pmatrix} \quad \text{and} \quad \begin{pmatrix} -7 & f & -13 & 3 \\ g & -15 & h & 2 \\ 3 & i & 5 & 1 \\ 2 & j & 4 & k \end{pmatrix}\]
which are inverses. Find the sum $a + b + c + d + e + f + g + h + i + j + k$.

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