
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
Consider a $4 \times 4$ matrix filled with each number from $1$ to $16$. Each number must be placed such that the entries in each row and in each column are in increasing order. Find the number of such matrices that exist.

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