
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
Two hundred people were surveyed. Of these, 160 indicated they liked Beethoven, and 130 indicated they liked Vivaldi. What is the minimum number of people surveyed who could have said they liked both Beethoven and Vivaldi?

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