
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
Let $a,$ $b,$ and $c$ be positive real numbers, and consider the expression
\[
2\frac{a + b}{c} + \frac{a + c}{b} + \frac{b + c}{a}.
\]
Find the minimum value of this expression.

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