
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
How many 14-step paths are there from $A$ to $D$ which pass through $B$ and then through $C$? The possible paths must traverse a grid-like structure with the following configuration:

[asy]
size(4cm,4cm);int w=10;int h=8;int i;pen p=fontsize(9);for (i=0; i<h; ++i){draw((0,i) -- (w-1,i));}for (i=0; i<w; ++i){draw((i, 0)--(i,h-1));}label("D", (w-1,0), SE, p);label("A", (0,h-1), NW, p);label("B", (4,5), NE, p);label("C", (7,2), NE, p);
[/asy]

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