
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
Given the equation:
\[ 3^{r} \cdot 7^{s}=[a, b, c]=[a, b, d]=[a, c, d]=[b, c, d] \]
find the number of such quadruples (as a function of \( r \) and \( s \)).

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