
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
You have a  $3 \times 2021$  chessboard from which one corner square has been removed. You also have a set of  $3031$  identical dominoes, each of which can cover two adjacent chessboard squares. Let  $m$  be the number of ways in which the chessboard can be covered with the dominoes, without gaps or overlaps.
What is the remainder when  $m$  is divided by  $19$ ?

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