
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 smallest value of  $M$  for which for any choice of positive integer  $n$  and positive real numbers  $x_1<x_2<\ldots<x_n \le 2023$  the inequality  $$ \sum_{1\le i < j \le n , x_j-x_i \ge 1} 2^{i-j}\le M $$  holds.

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