
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 modified shooting challenge, ten clay targets are set up in three columns with the first two columns containing four targets each, and the third column containing two targets. A marksman must adhere to the following rules:
1) The marksman starts by choosing one of the columns.
2) The shooter must then hit the lowest remaining target in the selected column.
Determine in how many different sequences the ten targets can be broken if the rules are strictly followed.

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