
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 16 into a $4 \times 4$ grid such that each number in a row is larger than the number to its left and each number in a column is larger than the number above it. Given that the numbers 4 and 13 are already placed in the grid, determine the number of different ways to fill the remaining 14 numbers.

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