
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 $1, 2, \cdots, 9$ into a $3 \times 3$ grid such that each cell contains one number, each row's numbers increase from left to right, and each column's numbers decrease from top to bottom. Find the total number of ways to achieve this.

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