
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
Determine all triples \((a, b, c)\) of positive integers for which the following conditions hold:

\[
\begin{aligned}
\operatorname{gcd}(a, 20) & = b, \\
\operatorname{gcd}(b, 15) & = c, \\
\operatorname{gcd}(a, c) & = 5.
\end{aligned}
\]

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