
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 natural number \( n \) with the following property: When selecting any 50 different numbers from \( 1, 2, \cdots, n \), there are always two numbers among these 50 numbers whose difference is 7. What is the maximum value of such \( n \)?

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