
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
Find the number of shortest paths from point \( O(0,0) \) to point \( P(10,5) \) in a coordinate grid that do not pass through any of the segments \( AB, CD, EF, GH \). The coordinates of \( A, B, C, D, E, F, G, H \) are respectively \( A(2,2), B(3,2) \), \( C(4,2), D(5,2) \), \( E(6,2), F(6,3) \), \( G(7,2), H(7,3) \).

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