
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 ten coins in her pocket: $3$ pennies, $3$ nickels, $3$ dimes, $1$ quarter, and $1$ half-dollar. She takes out two coins at a time, records the sum of their values, and then puts them back. She repeats this process for different pairs of coins. What is the maximum number of different sums she can record?

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