
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, there are three problems: A, B, and C. Among the 25 participating students, each student solves at least one problem. Among all the students who did not solve problem A, the number of students who solved problem B is twice the number of students who solved problem C. The number of students who only solved problem A is one more than the number of students who solved problem A among the remaining students. Among the students who solved only one problem, half did not solve problem A. How many students solved only problem B?

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