
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 math exam is conducted as follows. Each work is independently graded by three instructors, and each gives either 0 or 1 point for each problem. The computer then finds the arithmetic mean of the scores for each problem and rounds it to the nearest integer. The scores for all the problems are then summed up. It happened that in one of the works, each of the three experts gave 1 point for 3 problems and 0 points for all other problems. Find the highest possible total score for this work.

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