
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 purse: $3$ pennies, $1$ nickel, $2$ quarters, and $1$ half-dollar. She randomly picks two coins, sums their values, and records the result before putting them back. She continues this process multiple times. How many distinct sums can she record?

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