
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
Place 1 cent, 2 cents, 5 cents, and 10 cents coins into 19 boxes so that each box contains coins, and no two boxes contain the same total amount of money. How many coins are needed at a minimum? What is the minimum total value of all the coins in the boxes?

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