
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 setup, ten clay targets are arranged in four hanging columns with the configuration of three targets in the first and second column, two targets in the third column, and two targets in the fourth column. The rules for the marksman remain the same:
1) The marksman must choose one of the columns to shoot from.
2) The marksman must shoot the lowest remaining target in the chosen column.
Determine the number of different sequences in which all ten targets can be broken, while respecting the above-stated rules.

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