
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 problems $A$, $B$, and $C$, there are 39 participants, each of whom answered at least one question correctly. Among those who answered problem $A$ correctly, the number of participants who answered only problem $A$ is 5 more than those who also answered other problems. Among those who did not answer problem $A$ correctly, the number of participants who answered problem $B$ is twice the number of those who answered problem $C$. It is also given that the number of participants who answered only problem $A$ is equal to the sum of the participants who answered only problem $B$ and only problem $C$. What is the maximum number of participants who answered problem $A$?

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