
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 mathematics competition, three problems were given: $A$, $B$, and $C$. There were 25 students who each solved at least one problem. Among the students who did not solve problem $A$, twice as many solved $B$ as solved $C$. One more student solved only problem $A$ than the number of those who also solved problem $A$. Half of the students who solved only one problem did not solve $A$. How many students solved only problem $B$?

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