
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
An ancient British merchant had a 15-pound weight, which shattered into 4 pieces after falling to the ground. Each piece weighed an integer number of pounds, and it was possible to use these 4 pieces to measure any integer weight from 1 to 15 pounds (weights could only be placed on one side of the balance). What are the weights of the 4 pieces?

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