
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
Consider a grid where you can only move south and east. You need to find the number of paths from point $A$ to point $B$. The grid is 5 rows high and 10 columns wide. There are forbidden segments between points $(4,4)$ and $(4,3)$ and between points $(7,2)$ and $(7,1)$.

[asy]
import olympiad; size(300); defaultpen(linewidth(0.8)); dotfactor=4;
for(int i = 0; i <= 10; ++i)
if (i!=4 && i !=7)
draw((2*i,0)--(2*i,5));
for(int j = 0; j <= 5; ++j)
draw((0,j)--(20,j));

draw((2*4,2)--(2*4,3));
draw((2*7,1)--(2*7,2));

label("$A$",(0,5),NW);
label("$B$",(20,0),E);
[/asy]

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