
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 \( k \) integers 
\[ 1 \leq a_1 < a_2 < \cdots < a_k \leq n \]
be such that the least common multiple of any two numbers \( a_i, a_j \) is greater than \( n \). Then,
\[ \sum_{i=1}^{k} \frac{1}{a_i} < \frac{3}{2}. \]

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