
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
Expand the polynomial \((a + b + c + d + 1)^N\) (\(N \in \mathbb{Z}_{+}\)) and combine like terms to obtain 1001 terms, each of which includes positive integer powers of \(a\), \(b\), \(c\), and \(d\), and determine the value of \(N\).

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