
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 robotics club, only those who know mathematics, physics, or programming are accepted. It is known that 8 members of the club know physics, 7 know mathematics, and 11 know programming. Additionally, it is known that at least two people know both physics and mathematics, at least three know both mathematics and programming, and at least four know both physics and programming. What is the maximum possible number of participants in the club under these conditions?

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