
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 positive integer \( n (n \geq 2) \), find the maximum real number \( \lambda \) such that the inequality \( a_{n}^{2} \geq \lambda \left(a_{1}+a_{2}+\cdots+a_{n-1}\right) + 2 a_{n} \) holds for any positive integers \( a_{1}, a_{2}, \cdots, a_{n} \) satisfying \( a_{1} < a_{2} < \cdots < a_{n} \).

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