
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 are surveyed. Among these, 160 people indicated they liked Beethoven, and 150 people expressed they liked Chopin. What is the minimum number of people surveyed who could have said they liked both Beethoven and Chopin?

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