
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
Given a 4x4 matrix, all the digits from 1 through 16 are arranged such that the entries in every row and column are in increasing order, calculate the number of such matrices that exist.

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