
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
A robotics club accepts only those who know mathematics, physics, or programming. It is known that 8 members know physics, 7 members know mathematics, and 11 members know programming. Additionally, it is known that at least 2 members know both physics and mathematics, at least 3 members know both mathematics and programming, and at least 4 members know both physics and programming. What is the maximum number of club members under these conditions?

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