
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 an integer \( n \geq 4 \), find the minimum \( \lambda(n) \) such that for any set of non-negative real numbers \( a_1, a_2, \ldots, a_n \) with their sum equal to \( n \) (where subscripts are taken modulo \( n \)), it always holds that \( \sum_{i=1}^{n} \{ a_i \} a_{i+1} \leq \lambda(n) \).

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