
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
If \( b,c > 0 \) and \( a = b^2 \), find the smallest possible value of
\[
\left\lfloor{\frac{a+b}{c}}\right\rfloor + \left\lfloor{\frac{b+c}{a}}\right\rfloor + \left\lfloor{\frac{c+a}{b}}\right\rfloor.
\]
(Note that \( \left\lfloor{x}\right\rfloor \) denotes the greatest integer less than or equal to \( x \).)

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