
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
Determine the set of values for coefficients $p$, $q$, $r$ (and $s$) for which the polynomials resulting from the following products do not contain any terms with odd powers of $x$:
a) $\left(x^{3}-x^{2}-6x+2\right)\left(x^{3}+px^{2}+qx+r\right)$
b) $\left(x^{4}+cx^{3}+dx^{2}+ex+f\right)\left(x^{4}+px^{3}+qx^{2}+rx+s\right)$.

Write down the polynomial forms of the products for the found sets of values.

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