
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
Let  $n$  be a positive integer. In how many ways can a  $4 \times 4n$  grid be tiled with the following tetromino?
[asy]
size(4cm);
draw((1,0)--(3,0)--(3,1)--(0,1)--(0,0)--(1,0)--(1,2)--(2,2)--(2,0));
[/asy]

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