
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
The teacher wrote three different positive integers on the blackboard. Each time, Xiaoming first erases the first number and then writes the average of the other two numbers at the end. After doing this for 7 times, the sum of the three numbers on the blackboard becomes 195. If the sum of the three numbers on the blackboard at the beginning was 2013, and all the numbers written were positive integers, what was the first positive integer that the teacher wrote on the blackboard initially?

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