
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 consisting of problems $A$, $B$, and $C$, among the 39 participants, each person answered at least one problem correctly. Among the people who answered $A$ correctly, the number of people who only answered $A$ is 5 more than the number of people who answered other problems as well. Among the people who did not answer $A$ correctly, the number of people who answered $B$ is twice the number of people who answered $C$. Additionally, the number of people who only answered $A$ equals the sum of the number of people who only answered $B$ and the number of people who only answered $C$. What is the maximum number of people who answered $A$ correctly?

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