
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
In Chinese Chess, given a piece "Pawn" at point \( A \), the Pawn can move to point \( B \) along a certain path. Before crossing the river, the Pawn can only move to the intersection point directly in front of it at each step. After crossing the river, it can move to the intersection points directly in front, left, or right at each step but cannot move backward. The "river" refers to the area between the 5th and 6th horizontal lines on the board. If the Pawn does not pass through any intersection point more than once during its movement, the path is called a "non-repetitive path." How many different non-repetitive paths are there?

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