
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 $B$? Assume the grid is 10 units wide and 4 units tall, with two forbidden vertical segments removed from the grid as shown:
[asy]
import olympiad; size(250); defaultpen(linewidth(0.8)); dotfactor=4;
for(int i = 0; i <= 10; ++i)

if (i!=5 && i !=6)

draw((2i,0)--(2i,4));
for(int j = 0; j <= 4; ++j)

draw((0,j)--(20,j));

draw((2*5,0)--(2*5,1));
draw((2*6,0)--(2*6,1));
draw((2*5,3)--(2*5,4));
draw((2*6,3)--(2*6,4));

label("$A$",(0,4),NW);
label("$B$",(20,0),E);
draw("$N$",(22,1.0)--(22,3.5),3N,EndArrow(4));
draw((21.7,1.3)--(22.3,1.3));
[/asy]

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