
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 survey of $150$ people, $90$ had migraines, $60$ had insomnia, and $30$ had anxiety. It was also found that:
- $20$ had both migraines and insomnia,
- $10$ had both migraines and anxiety,
- $15$ had both insomnia and anxiety,
- $5$ had all three conditions: migraines, insomnia, and anxiety.

How many people surveyed had none of these conditions?

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