
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  $f(x)=x^{2007}+17x^{2006}+1$  has distinct zeroes  $r_1,\ldots,r_{2007}$ .  A polynomial  $P$  of degree  $2007$  has the property that  $P\left(r_j+\dfrac{1}{r_j}\right)=0$  for  $j=1,\ldots,2007$ .  Determine the value of  $P(1)/P(-1)$ .

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