
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 \((x-1)\left(x^{2}-1\right)\left(x^{3}-1\right) \cdots\left(x^{2007}-1\right)\) is expanded, and the terms with degree greater than 2007 are removed. The resulting polynomial is denoted as \(f(x)\). Find the degree and the leading coefficient of \(f(x)\).

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