
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
There is a stack of $n$ cards, numbered from $1$ to $n$ from top to bottom. Each time you can extract a small stack of cards (which can consist of just one card) without disturbing their order and insert them back into the stack at any position (either between two cards, on top of the first card, or below the $n$th card). This operation is called an extraction. What is the minimum number of extractions required to completely reverse the order of the stack, such that the $n$ cards are numbered $n$, $n-1, \cdots, 2, 1$ from top to bottom?

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