
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
Five girls — Mary, Alina, Tina, Hanna, and Emma — sang songs in a concert as quartets, with one girl sitting out each time. Hanna sang $10$ songs, which was more than any other girl, and Mary sang $5$ songs, which was fewer than any other girl. Determine the number of songs these quartets sang.

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