
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
A game board consists of $81$ squares arranged in a 9x9 grid, with squares alternating in color between black and white. Square $P$ is located in the bottom row and square $Q$ in the top row. A marker is placed on square $P$. A step consists of moving the marker to one of the adjoining white squares in the row directly above, either straight up, up-and-left, or up-and-right. Calculate the number of $8$-step paths from $P$ to $Q$.

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