
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
Moving only south and east along the line segments, how many paths are there from \( A \) to \( B \) on a grid shown below? Assume there are horizontal lines from 0 to 5 and vertical lines from 0 to 7. Two forbidden segments are present, as detailed below:

[Insert hypothetical diagram here]
- Grid size: \( 5 \times 7 \)
- Forbidden segment 1 blocks between \( (3,4) \) and \( (4,4) \)
- Forbidden segment 2 blocks between \( (2,2) \) and \( (3,2) \)
  
Label point \( A \) at \( (0,5) \) and point \( B \) at \( (7,0) \).

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