
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, ten clay targets are arranged in three hanging columns with four targets in the first column, three in the second column, and three in the third column. A shooter must follow these rules:
1) The shooter selects one column from which a target will be broken.
2) The shooter must break the lowest remaining target in the chosen column.
Determine the number of different sequences in which all ten targets can be broken.

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