
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
\[ 
\begin{pmatrix} 
1 & a & 2 \\ 
b & 3 & c \\ 
4 & d & 5 
\end{pmatrix} 
\quad \text{and} \quad 
\begin{pmatrix} 
-7 & e & f \\ 
-6 & -15 & g \\ 
3 & h & 6 
\end{pmatrix}
\] are inverses. Find \(a + b + c + d + e + f + g + h.\)

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