
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
The first  $9$  positive integers are placed into the squares of a  $3\times 3$  chessboard. We are taking the smallest number in a column. Let  $a$  be the largest of these three smallest number. Similarly, we are taking the largest number in a row. Let  $b$  be the smallest of these three largest number. How many ways can we distribute the numbers into the chessboard such that  $a=b=4$ ?

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