
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
Let \( q(x) = q^1(x) = 2x^2 + 2x - 1 \), and let \( q^n(x) = q(q^{n-1}(x)) \) for \( n > 1 \). How many negative real roots does \( q^{2016}(x) \) have?

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