
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 \(n \geq 2\), find the largest real number \(\lambda\) such that the inequality 
\[ a_{n}^{2} \geq \lambda\left(a_{1} + a_{2} + \cdots + a_{n-1}\right) + 2a_{n} \]
holds for any integers \( a_{1}, a_{2}, \cdots, a_{n} \) satisfying \( 0 < a_{1} < a_{2} < \cdots < a_{n} \).

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