
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 five identical, dotless dominoes (shaded 1 by 2 rectangles) on a 6 by 5 grid so that a path is formed from the upper left-hand corner $A$ to the lower right-hand corner $B$. In the path, consecutive dominoes must touch at their sides, not just corners. No domino can be placed diagonally; each domino must cover exactly two of the unit squares shown in the grid. How many distinct arrangements are possible, ensuring all dominoes are used in the path?

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