
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
Find the number of triplets of natural numbers \((a, b, c)\) that satisfy the system of equations:

\[ 
\begin{cases} 
\gcd(a, b, c) = 21 \\
\operatorname{lcm}(a, b, c) = 3^{17} \cdot 7^{15} 
\end{cases} 
\]

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