
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
Given that the polynomial  $P(x) = x^5 - x^2 + 1$  has  $5$  roots  $r_1, r_2, r_3, r_4, r_5$ . Find the value of the product  $Q(r_1)Q(r_2)Q(r_3)Q(r_4)Q(r_5)$ , where  $Q(x) = x^2 + 1$ .

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