
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 math competition, 30 students participated. From these students:

- 20 solved the 1st problem,
- 16 solved the 2nd problem,
- 10 solved the 3rd problem,
- 11 solved both the 1st and the 2nd problems,
- 7 solved both the 1st and the 3rd problems,
- 5 solved both the 2nd and the 3rd problems,
- 4 solved all three problems.

How many students participated in the competition who did not solve any problems at all?

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