
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 \( n \geq 5 \), and \( n \) distinct natural numbers \( a_{1}, a_{2}, \ldots, a_{n} \) which satisfy the condition: for any two different non-empty subsets \( A \) and \( B \) of the set \( S = \{ a_{1}, a_{2}, \ldots, a_{n} \} \), the sum of the numbers in \( A \) is not equal to the sum of the numbers in \( B \). Under this condition, find the maximum value of the reciprocal sum
$$
\frac{1}{a_{1}} + \frac{1}{a_{2}} + \cdots + \frac{1}{a_{n}}
$$.

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