
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 smallest possible value of the expression $$\frac{(a+2b)^2+(b-2c)^2+(c-2a)^2}{b^2},$$ where \( b > c > a \) are real numbers, and \( b \neq 0 \).

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