
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 middle school math competition, there were three problems labeled A, B, and C. Among the 25 students who participated, each student solved at least one problem. Among the students who did not solve problem A, the number who solved problem B was twice the number of those who solved problem C. The number of students who solved only problem A was one more than the number of students who solved A along with any other problem. 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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