
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
Given the set \(X = \{1, 2, \cdots, k\}\), for a subset \(A \subseteq X\), let \(S(A)\) denote the sum of all elements in \(A\). The set \(X\) is divided into two disjoint subsets \(A\) and \(B\), with \(A \cup B = X\). If \(S(A) = 2S(B)\), find all possible values of \(k\).

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