
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
Find the largest real constant $\lambda$ such that for any positive integer $n$ and for positive real numbers $x_{1}, x_{2}, \cdots, x_{n}$ that satisfy $\sum_{i=1}^{n} \frac{1}{x_{i}}=n$, the following inequality always holds: $\prod_{i=1}^{n} x_{i}-1 \geqslant \lambda\left(\sum_{i=1}^{n} x_{i}-n\right)$.

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