
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
Determine the maximum real number \( C \) such that
$$
\sum_{i=1}^{n} \frac{x_{i}}{x_{i-1}} \geq n + C,
$$
for all positive integers \( n \) and all sequences of positive real numbers \( x_{0}, x_{1}, \ldots, x_{n} \) such that \( x_{0} = 1 \) and \( x_{n} = 2 \).

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