
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 collection of coins in her wallet: 3 pennies, 2 nickels, 2 dimes, 1 quarter, and 1 half-dollar. She randomly picks two coins, records the sum of their values, and then returns them to her wallet. She repeats this process multiple times. What is the maximum number of different sums she can record?

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