
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 \( a, b, c, d \) be strictly positive real numbers satisfying \( (a+c)(b+d)=ac+bd \). Determine the smallest value that

\[ 
\frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} 
\]

can take.

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