
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 $g(x)=x^{2010}+14x^{2009}+1$ has distinct zeroes $s_1,\ldots,s_{2010}$. A polynomial $Q$ of degree $2010$ has the property that
\[Q\left(s_j+\dfrac{1}{s_j}\right)=0\] for $j=1,\ldots,2010$. Determine the value of $\frac{Q(1)}{Q(-1)}$.

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