
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
Let $[r,s]$ denote the least common multiple of positive integers $r$ and $s$. Find the number of ordered quadruples $(a,b,c,d)$ of positive integers for which $[a,b] = 900$, $[b,c] = 1800$, $[c,d] = 3600$, and $[d,a] = 1200$.

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