
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 15-step paths are from $A$ to $D$, which pass through $C$? Here in the grid, $A$ is at the top left corner, $C$ is 4 squares to the right and 3 squares down from $A$, and $D$ is at the bottom right corner of a grid of size 7x9.

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