
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 how many ways can we enter numbers from the set  $\{1,2,3,4\}$  into a  $4\times 4$  array so that all of the following conditions hold?

(a) Each row contains all four numbers.

(b) Each column contains all four numbers.

(c) Each "quadrant" contains all four numbers.  (The quadrants are the four corner  $2\times 2$  squares.)

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