
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 $[r, s]$ represent the least common multiple of integers $r$ and $s$. Find the number of ordered triples of positive integers $(a, b, c)$ such that $[a, b] = 1000$, $[b, c] = 2000$, and $[c, a] = 2000$.

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