
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
What is the sign of the $n$-th term in the expansion of the product

$$(1-a)(1-b)(1-c)(1-d) \ldots=1-a-b+a b-c+a c+b c-a b c-d+\ldots$$

for $n = 0, 1, 2, \ldots$?

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