
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
Suppose you have a grid as shown below, how many 15-step paths are there from point $H$ to point $J$ which pass through point $I$?
[asy]
size(5cm,5cm);
int w=9;
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("J", (w-1,0), SE, p);
label("H", (0,h-1), NW, p);
label("I", (5,5), NE, p);
[/asy]

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