
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 point \(A\) to point \(B\)? Consider the following grid diagram, where broken lines indicate forbidden paths. The grid is extended to 5 rows tall and 11 columns wide:
\[ \text{[Grid description not necessary for visualization in text format]} \]
There are broken lines extending:
- from \(2, 0\) to \(2, 1\)
- from \(5, 0\) to \(5, 3\)
- from \(7, 2\) to \(7, 4\)
Points \(A\) and \(B\) are located at the top left and the bottom right corners of the grid, respectively.

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