
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
There are 25 students in a summer camp who are participating in activities like swimming, archery, and chess. Each student is involved in at least one of these activities but can participate in two or all three of them. There are 15 students participating in swimming, 17 in archery, and 10 in chess. If 12 students are involved in at least two activities, determine the number of students taking all three activities.

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