
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
The atelier "Tyazhka Nosh" purchased a large batch of cast-iron buttons. If they sew two buttons on each coat or if they sew three buttons on each coat, then 1 button will remain from the entire batch in each case. If they sew four buttons on each coat or if they sew five buttons on each coat, then 3 buttons will remain from the entire batch in each case. How many buttons will remain if they sew twelve buttons on each coat?

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