
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
Matt will arrange four identical, dotless dominoes (shaded 1 by 2 rectangles) on a 6 by 4 grid so that a path is formed from the upper left-hand corner $A$ to the lower right-hand corner $B$. In a path, consecutive dominoes must touch at their sides and not just their corners. No domino may be placed diagonally; each domino covers exactly two of the unit squares shown on the grid. How many distinct arrangements are possible?

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