
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
For the binomial \\((1-x)^{1999}\\), there are the following four propositions:

\\(①\\) In the expansion, \\(T_{1000} = -C_{1999}^{1000}x^{999}\\);

\\(②\\) In the expansion, the sum of the coefficients of the non-constant terms is \\(1\\);

\\(③\\) In the expansion, the terms with the largest coefficients are the \\(1000^{th}\\) and \\(1001^{st}\\) terms;

\\(④\\) When \\(x=2000\\), the remainder of \\((1-x)^{1999}\\) divided by \\(2000\\) is \\(1\\).

Among these propositions, the correct ones are ___________\\(.(\\) Fill in all the correct proposition numbers \\()\\)

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