
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
The polynomial  $Q(x)=x^3-21x+35$  has three different real roots. Find real numbers  $a$  and  $b$  such that the polynomial  $x^2+ax+b$  cyclically permutes the roots of  $Q$ , that is, if  $r$ ,  $s$  and  $t$  are the roots of  $Q$  (in some order) then  $P(r)=s$ ,  $P(s)=t$  and  $P(t)=r$ .

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