
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 each cell of the table  $4 \times 4$ , in which the lines are labeled with numbers  $1,2,3,4$ , and columns with  letters  $a,b,c,d$ ,  one number is written:  $0$  or  $1$  . Such a table is called *valid* if there are exactly two units in each of its rows and in each column. Determine the number of *valid* tables.

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