
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 there from $A$ to $D$ which pass through both $B$ and $C$ on a square grid? Assume $A$, $B$, $C$, and $D$ are positioned such that:
- $A$ is at the top left corner.
- $B$ is 2 steps to the right and 3 steps down from $A$.
- $C$ is 4 steps to the right and 1 step down from $B$.
- $D$ is 3 steps to the right and 2 steps down from $C$.

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