
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
In a group of 120 people, 95 indicated they liked Beethoven, and 80 indicated they liked Vivaldi. What is the minimum number of people in this survey who could have said they liked both Beethoven and Vivaldi?

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