
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 columns with the first column having four targets, the second having three targets, and the third having three targets. A marksman is to break all the targets following these rules:
1) The marksman must alternate between choosing a target from column one and column two for the first two shots and then continue with any column.
2) The marksman must then break the lowest remaining target in the chosen column.
In how many different orders can the ten targets be broken?

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