
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 largest constant \( C > 0 \) satisfying the following property:

For any 2023-tuple \(\left(a_{1}, a_{2}, \ldots, a_{2023}\right)\) of pairwise distinct, strictly positive real numbers, the following inequality holds:

$$
\frac{a_{1}}{\left|a_{2}-a_{3}\right|}+\frac{a_{2}}{\left|a_{3}-a_{4}\right|}+\ldots+\frac{a_{2023}}{\left|a_{1}-a_{2}\right|}>C
$$

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