
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 Mozart, $120$ indicated they liked Bach, and $90$ indicated they liked Beethoven. What is the minimum number of people surveyed who could have said they liked both Mozart and Bach, but not Beethoven?

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