
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
It is given the equation  $x^2+px+1=0$ , with roots  $x_1$  and  $x_2$ ;

(a) find a second-degree equation with roots  $y_1,y_2$  satisfying the conditions  $y_1=x_1(1-x_1)$ ,  $y_2=x_2(1-x_2)$ ;
(b) find all possible values of the real parameter  $p$  such that the roots of the new equation lies between  $-2$  and  $1$ .

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