
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 with a total of three problems, A, B, and C, each of the 25 participating students solved at least one problem. Among the students who didn't 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 solved only 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 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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