
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, eight clay targets are set up in three hanging columns with the configuration: three targets in the first column, two targets in the second column, and three targets in the third column. A shooter must hit all the targets following these rules:
1) The shooter selects any one of the columns to shoot a target from.
2) The shooter must then hit the lowest remaining target in the selected column.
How many different sequences can the shooter follow to break all eight targets?

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