
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 $3 \times 3$ grid, each $1 \times 1$ cell needs to be filled with a number. The number in the top right corner is already filled and is 30. The numbers to be filled must satisfy the following conditions:
(1) Each number must be a divisor of the number in the cell directly above it (if such a cell exists).
(2) Each number must be a divisor of the number in the cell directly to its right (if such a cell exists).

How many different ways are there to fill the grid?

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