
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 boy has the following coins in his pocket: $4$ pennies, $2$ nickels, $1$ dime, and $2$ quarters, and a half-dollar coin (50 cents). He takes out two coins, records the sum of their values, and then returns them to his pocket. He continues to choose two coins, record the sum, and put them back. What is the maximum number of different sums he can record?

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