
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
Find all pairs \((r, s)\) of real numbers such that the zeros of the polynomials
\[ f(x)=x^{2}-2rx+r \]
and
\[ g(x)=27x^{3}-27rx^{2}+sx-r^{6} \]
are all real and nonnegative.

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