
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
For an array of distinct integers $(i_1, i_2, \ldots, i_n)$ (where $n$ is a positive integer not less than 2), if $i_p > i_q$ when $p < q$, then $i_p$ and $i_q$ are considered an "inversion" in the array. The total number of "inversions" in an array is called the "inversion number" of the array. For example, the array $(2, 4, 3, 1)$ has inversions "2,1", "4,3", "4,1", "3,1", and its "inversion number" is 4. If the "inversion number" of an array of distinct positive integers $(a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8)$ is 2, then the "inversion number" of $(a_8, a_7, a_6, a_5, a_4, a_3, a_2)$ is at least    ．

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