
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
Fill the numbers $1$ to $9$ into a $3 \times 3$ grid, such that in each row, the number to the right is greater than the number to the left, and in each column, the number below is greater than the number above. Given that $1$, $4$, and $9$ are already placed in the grid, determine the number of different ways to fill the remaining 6 integers.

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