
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
Consider a  $9 \times 9$  grid of squares. Haruki fills each square in this grid with an integer between 1 and 9, inclusive.  The grid is called a  $\textit{super-sudoku}$  if each of the following three conditions hold:



- Each column in the grid contains each of the numbers  $1, 2, 3, 4, 5, 6, 7, 8, 9$  exactly once.
- Each row in the grid contains each of the numbers  $1, 2, 3, 4, 5, 6, 7, 8, 9$  exactly once.
- Each  $3 \times 3$  subsquare in the grid contains each of the numbers  $1, 2, 3, 4, 5, 6, 7, 8, 9$  exactly once.

How many possible super-sudoku grids are there?  

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