
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 a positive integer \( n \), let the set \( M = \{0, \pm 1, \pm 2, \cdots, \pm n\} \). A subset \( P \) of \( M \) is called a "basis subset" if every element in \( M \) can be expressed as the sum of some (possibly one) distinct elements of \( P \). Find the smallest positive integer \( k \) such that any \( k \)-element subset of \( M \) is a basis subset.

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