
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
A sequence \( (i_{1}, i_{2}, \ldots, i_{n}) \) is composed of the first \( n \) natural numbers, arranged in random order. Find the average number of inversions in this sequence, where an inversion is defined as any pair of numbers \( i_{j} > i_{k} \) such that \( j < k \).

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