
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 a square table consisting of 2015 rows and columns, positive numbers are arranged. The product of the numbers in each row and in each column is equal to 1, and the product of the numbers in any 1008 x 1008 square is equal to 2. What is the number in the center of the table?

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