
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
Let the set \( M = \{1, 2, 3, \cdots, 50\} \). For any subset \( S \subseteq M \) such that for any \( x, y \in S \) with \( x \neq y \), it holds that \( x + y \neq 7k \) for any \( k \in \mathbf{N} \). If \( S_0 \) is the subset with the maximum number of elements that satisfies this condition, how many elements are there in \( S_0 \)?

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