
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 shooting competition, nine clay targets are set up in three hanging columns. The first column contains four targets, the second column contains three targets, and the third column contains two targets. A sharpshooter must break all the targets under the following conditions:
1) The sharpshooter first selects any one of the columns from which a target is to be broken.
2) The sharpshooter must then break the lowest remaining target in the chosen column.
What are the different possible orders in which the sharpshooter can break all nine targets?

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