
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 are 10 children of different heights standing in a circle. Occasionally, one of them moves to another position (between some two children). The children want to arrange themselves in increasing order of height clockwise (from the shortest to the tallest) as quickly as possible. What is the minimum number of such moves needed, regardless of their initial positions?

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