
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
One hundred and twenty people were surveyed. Of these, $95$ indicated they liked Mozart and $80$ indicated they liked Beethoven. What is the minimum number of people surveyed who could have said they liked both Mozart and Beethoven, knowing at least 10 people do not like either?

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