
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 \( n \) distinct natural numbers \( a_{1}, a_{2}, \ldots, a_{n} \) have the following property: for any two different non-empty subsets \( A \) and \( B \) of the set
\[ S = \{a_{1}, a_{2}, \ldots, a_{n} \} \]
the sums of all the numbers in \( A \) and \( B \) are not equal. Under these conditions, find the maximum value of
\[ \frac{1}{a_{1}} + \frac{1}{a_{2}} + \cdots + \frac{1}{a_{n}}. \]

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