
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
 $39$  students participated in a math competition. The exam consisted of  $6$  problems and each problem was worth  $1$  point for a correct solution and  $0$  points for an incorrect solution. For any  $3$  students, there is at most  $1$  problem that was not solved by any of the three. Let  $B$  be the sum of all of the scores of the  $39$  students. Find the smallest possible value of  $B$ .

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