
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
\[
\begin{pmatrix} a & 2 & b \\ 3 & 3 & 4 \\ c & 6 & d \end{pmatrix} 
\quad \text{and} \quad 
\begin{pmatrix} -6 & e & -12 \\ f & -14 & g \\ 3 & h & 5 \end{pmatrix}
\]
are inverses. Find \( a + b + c + d + e + f + g + h \).

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