
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 a quadratic equation in $x$, $(n+1)x^2 + x - n = 0$, where its two real roots are $a_n$ and $b_n$ ($n$ is a positive integer), calculate the value of $a_1 \cdot a_2 \cdot a_3 \cdots a_{2011} \cdot b_1 \cdot b_2 \cdot b_3 \cdots b_{2011}$.

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