
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
A  $3\times 6$  grid is filled with the numbers in the list  $\{1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9\}$  according to the following rules:  (1)  Both the first three columns and the last three columns contain the integers 1 through 9.  (2) No numbers appear more than once in a given row.  Let  $N$  be the number of ways to fill the grid and let  $k$  be the largest positive integer such that  $2^k$  divides  $N$ .  What is k?

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