
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 an enhanced shooting match, ten clay targets are arranged with three columns, the first having four targets, the second having four targets, and the third having two targets. A marksman must break all the targets following these rules:
1) The marksman selects one column from which to break a target.
2) The marksman must break the lowest remaining target in the chosen column.
Determine the number of different orders in which the ten targets can be broken.

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