
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
Compute the matrix product and then add a scalar product
\[
\left(\begin{pmatrix} 0 & d & -b \\ -d & 0 & a \\ b & -a & 0 \end{pmatrix} + \begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{pmatrix}\right) \begin{pmatrix} d^2 & db & dc \\ db & b^2 & bc \\ dc & bc & c^2 \end{pmatrix}.
\]

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