
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
A girl has the following coins in her wallet: 2 pennies, 2 nickels, 1 quarter, and 2 half dollars. She randomly picks two coins, calculates the total value of these two coins, records it, and then puts them back with the other coins. This process is repeated multiple times. What is the maximum number of different sums that she can record?

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