
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 eight coins in her purse: $3$ pennies, $1$ nickel, $2$ dimes, $1$ quarter, and $1$ half-dollar. She takes out two coins, records the sum of their values, and then puts them back with the other coins. She continues to take out two coins, record the sum of their values, and put them back. How many different sums can she record at most?

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