
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 \( S_{n} \) denote certain subsets of the set of positive integers \( \{1, 2, 3, \cdots, 100\} \) that satisfy the condition: no number in the subset is twice any other number. What is the maximum number of elements that such a subset can contain?

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