
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 three real numbers \(a < b < c\) satisfying:
\[
\begin{aligned}
a + b + c & = \frac{21}{4} \\
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} & = \frac{21}{4} \\
abc & = 1
\end{aligned}
\]

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