
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 match, ten clay targets are arranged in three hanging columns with four targets in the first column, three in the second, and three in the third. A marksman is to break all the targets following these 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 ten targets be broken if the rules are followed?

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