
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 \( M = \{1, 2, \cdots, k\} \), for any subset \( A \subseteq M \), let \( S(A) \) denote the sum of all elements in \( A \). If it is possible to partition \( M \) into two disjoint subsets \( A \) and \( B \), where \( A \cup B = M \) and \( S(A) = 2S(B) \), find all possible values of \( k \).

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