
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
How many ways are there to fill the  $2 \times 2$  grid below with  $0$ 's and  $1$ 's such that no row or column has duplicate entries?

[asy]
	size(2cm);
	draw(unitsquare);
	draw( (0.5,0)--(0.5,1) );
	draw( (0,0.5)--(1,0.5) );
[/asy]

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