
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
Determine for which positive integers \( k \) the set
\[ 
X = \{1990, 1990+1, 1990+2, \ldots, 1990+k\} 
\]
can be partitioned into two disjoint subsets \( A \) and \( B \) such that the sum of the elements of \( A \) is equal to the sum of the elements of \( B \).

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