
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 four propositions:  
① The term $T_{1000} = -C_{1999}^{1000}x^{999}$;  
② The sum of the coefficients of the non-constant terms is 1;  
③ The terms with the largest coefficients are the 1000th and 1001st terms;  
④ When $x=2000$, the remainder of $(1-x)^{1999}$ divided by 2000 is 1. The correct propositions are.

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