
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
Calculate the following matrix product:
\[
\begin{pmatrix} 0 & d & -e \\ -d & 0 & f \\ e & -f & 0 \end{pmatrix} 
\begin{pmatrix} a^3 & a^2b & a^2c \\ ab^2 & b^3 & b^2c \\ ac^2 & bc^2 & c^3 \end{pmatrix}.
\]

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