
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
 $2016$  numbers written on the board:  $\frac{1}{2016}, \frac{2}{2016}, \frac{3}{2016},  ..., \frac{2016}{2016}$ . In one move, it is allowed to choose any two numbers  $a$  and  $b$  written on the board, delete them, and write the number  $3ab - 2a - 2b + 2$  instead. Determine what number will remain written on the board after  $2015$  moves.

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