
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 $n > 1$ be a given integer. Find the largest constant $\lambda(n)$ such that for any $n$ nonzero complex numbers $z_{1}, z_{2}, \cdots, z_{n}$, the following inequality holds:
$$
\sum_{k=1}^{n}\left|z_{k}\right|^{2} \geqslant \lambda(n) \min_{1 \leq k \leq n}\left\{\left|z_{k+1} - z_{k}\right|^{2}\right\} \quad \text{where} \quad z_{n+1} = z_{1}.
$$

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