
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]


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Three problems \( A \), \( B \), and \( C \) were given on a mathematics olympiad. All 25 students solved at least one of these problems. The number of students who solved \( B \) and not \( A \) is twice the number of students who solved \( C \) and not \( A \). The number of students who solved only \( A \) is greater by 1 than the number of students who, along with \( A \), solved at least one other problem. Among the students who solved only one problem, half solved \( A \). How many students solved only \( B \)?

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