
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 positive integer  $n$ , find the biggest real number  $C$  which satisfy the condition that if the sum of the reciprocals of a set of integers (They can be the same.) that are greater than  $1$  is less than  $C$ , then we can divide the set of numbers into no more than  $n$  groups so that the sum of reciprocals of every group is less than  $1$ .

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