
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 bug travels from Point A to Point C on a modified hexagonal lattice. The segments marked with an arrow are uni-directional, and the bug must not traverse any segment more than once. Along its path, it must also pass Point B. Calculate the number of unique paths available.

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