
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 the matrices
\[\begin{pmatrix} 2a & 2 & 3b \\ 1 & 3 & 2 \\ d & 4 & c \end{pmatrix} \quad \text{and} \quad \begin{pmatrix} -10 & e & -15 \\ f & -20 & g \\ 3 & h & 5 \end{pmatrix}\]
are inverses. Find $a + b + c + d + e + f + g + h$.

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