
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 the magical land of Oz, the mathematics exam is graded as follows. Each submission is independently reviewed by three instructors, and each gives a score of either 0 or 1 for each problem. A computer then calculates the arithmetic mean of the scores for each problem and rounds it to the nearest integer. The scores for all problems are then summed. 

It happened that in one submission, each of the three instructors gave a score of 1 for 3 problems and a score of 0 for all other problems. Find the maximum possible total score for this submission.

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