
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
A pharmacist needs to create a mixture from three components \( A \), \( B \), and \( C \) with the following composition: \( a\% \) \( A \), \( b\% \) \( B \), \( c\% \) \( C \). However, he does not have the pure substances \( A \), \( B \), and \( C \). Instead, he has three different mixtures of these substances with the following compositions:
1) \( a_{1}\% \) \( A \), \( b_{1}\% \) \( B \), \( c_{1}\% \) \( C \);
2) \( a_{2}\% \) \( A \), \( b_{2}\% \) \( B \), \( c_{2}\% \) \( C \);
3) \( a_{3}\% \) \( A \), \( b_{3}\% \) \( B \), \( c_{3}\% \) \( C \).

How should he create the needed mixture? Address this problem using the Gibbs triangle. You can limit your consideration to the specific case where:

\[
\begin{array}{rlr}
a_{1}=10, & b_{1}=30, & c_{1}=60 \\
a_{2}=20, & b_{2}=60, & c_{2}=20 \\
a_{3}=80, & b_{3}=10, & c_{3}=10 \\
a=50, & b=30, & c=20
\end{array}
\]

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