
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
At a math competition, three problems were presented: \(A\), \(B\), and \(C\). There were 25 students, each of whom solved at least one problem. Among the students who did not solve problem \(A\), twice as many solved problem \(B\) as those who solved problem \(C\). Exactly one more student solved only problem \(A\) than the number of other students who also solved \(A\). Half of the students who solved only one problem 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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