
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
An L-shaped region is formed by attaching two  $2$  by  $5$  rectangles to adjacent sides of a  $2$  by  $2$  square as shown below.
[asy] size(6cm);
draw((0,0)--(7,0)--(7,2)--(2,2)--(2,7)--(0,7)--cycle);
real eps = 0.45;
draw(box( (0,0), (eps,eps) ));
draw(box( (7,0), (7-eps,eps) ));
draw(box( (7,2), (7-eps,2-eps) ));
draw(box( (0,7), (eps,7-eps) ));
draw(box( (2,7), (2-eps,7-eps) ));
label(" $7$ ", (0,3.5), dir(180));
label(" $7$ ", (3.5,0), dir(270));
label(" $2$ ", (7,1), dir(0));
label(" $5$ ", (4.5,2), dir(90));
label(" $5$ ", (2,4.5), dir(0));
label(" $2$ ", (1,7), dir(90));
[/asy]
The resulting shape has an area of  $24$  square units.  How many ways are there to tile this shape with  $2$  by  $1$  dominos (each of which may be placed horizontally or vertically)?

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