
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
Regarding the binomial $$( \sqrt {x}-1)^{2005}$$, the following propositions are made:  
① The sum of the coefficients of the non-constant terms in the binomial expansion is 1;  
② The sixth term of the binomial expansion is $$C_{ 2005 }^{ 6 }\cdot x^{1999}$$;  
③ There are no rational terms in the binomial expansion;  
④ When x=100, the remainder of $$( \sqrt {x}-1)^{2005}$$ divided by 100 is 49.  
Among these, the correct proposition numbers are \_\_\_\_\_\_ . (Note: Fill in all the proposition numbers you think are correct)

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