
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
In a revised shooting match, nine clay targets are arranged in three hanging columns; the first two columns each contain three targets, and the third column has three targets. A marksman must break all the targets following the rules:
1) The marksman first chooses a column from which a target is to be broken.
2) The marksman must then break the lowest remaining target in the chosen column.
How many different orders can the nine targets be broken, following these rules?

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