
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 the polynomial \(1 - x + x^{2} - x^{3} + \cdots + x^{16} - x^{17}\), express it in the form \(a_{0} + a_{1} y + a_{2} y^{2} + a_{3} y^{3} + \cdots + a_{16} y^{16} + a_{17} y^{17}\), where \(y = x + 1\), and each \(a_{i}\) is a constant. Find \(a_{2}\).

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