
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

Let $[a_1, a_2, \cdots, a_n]$ be a permutation of $1, 2, \cdots, n$. If $a_i > a_j$ holds for all $j > i$, then $a_i$ is called a "large" number in this permutation. Compute the arithmetic mean of all the "large" numbers over all permutations of length $n$.

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