
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
Jessica is tasked with placing four identical, dotless dominoes on a 4 by 5 grid to form a continuous path from the upper left-hand corner \(C\) to the lower right-hand corner \(D\). The dominoes are shaded 1 by 2 rectangles that must touch each other at their sides, not just at the corners, and cannot be placed diagonally. Each domino covers exactly two of the unit squares on the grid. Determine how many distinct arrangements are possible for Jessica to achieve this, assuming the path only moves right or down.

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