
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 \( n \geq 5 \) be a natural number, and let \( a_{1}, a_{2}, \cdots, a_{n} \) be \( n \) distinct natural numbers with the following property: for any two distinct non-empty subsets \( A \) and \( B \) of the set \( S = \{a_{1}, a_{2}, \cdots, a_{n}\} \), the sum of all the numbers in \( A \) is not equal to the sum of all the numbers in \( B \). Under these conditions, determine the maximum value of \( \frac{1}{a_{1}}+\frac{1}{a_{2}}+\cdots+\frac{1}{a_{n}} \). (1994 Shanghai Competition Problem)

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