
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
Thirty soldiers escaped. Five artillerymen, five dragoons, five grenadiers, and 15 common soldiers were captured. The General sentenced fifteen of them to death, and left it to the Colonel to arrange them in such a way that, starting from the left and counting every ninth soldier, he would shoot them dead. Once he reaches the end of the line, counting continues from the beginning until the entire group of 30 has been reduced to 15, who are then spared. The Colonel wanted to save the artillerymen, grenadiers, and dragoons. What arrangement did he use?

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