
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 mathematics competition, three problems $A, B, C$ were posed and 25 students participated. Each student solved at least one problem. Among students who did not solve problem $A$, the number of students who solved problem $B$ is twice the number who solved problem $C$. Among students who solved problem $A$, the number of students who solved only problem $A$ is one more than the number of those who, in addition to problem $A$, solved other problems. Additionally, among students who solved only one problem, half of them 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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