
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
In a $6 \times 6$ grid as shown, fill the numbers $1$ to $6$ in the blank squares so that each number from $1$ to $6$ appears exactly once in each row and each column. Some numbers have already been filled in the grid. How many ways are there to fill the remaining blank squares to meet these requirements?

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