
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 distinct non-zero real numbers satisfying the following two conditions: $ac = bd$  and   $\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}= 4$ .
Determine the largest possible value of the expression  $\frac{a}{c}+\frac{c}{a}+\frac{b}{d}+\frac{d}{b}$ .


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