
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
Given a sequence of distinct positive integers $(i\_1, i\_2, \ldots, i\_n)$ where $n$ is a positive integer greater than or equal to 2, if $i\_p > i\_q$ when $p > q$, then $i\_p$ and $i\_q$ are called a "good order" of the sequence. The number of "good orders" in a sequence is called the "good order number" of that sequence. For example, the sequence (1, 3, 4, 2) has "good orders" "1, 3", "1, 4", "1, 2", "3, 4", so its "good order number" is 4. If the "good order number" of the sequence of distinct positive integers $(a\_1, a\_2, a\_3, a\_4, a\_5, a\_6, a\_7)$ is 3, then the "good order number" of $(a\_7, a\_6, a\_5, a\_4, a\_3, a\_2, a\_1)$ is $\_\_\_\_\_\_\_.$

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