
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
Given the following three inequalities: (①$ab>0$); (②$\frac{c}{a}>\frac{d}{b}$); (③$bc>ad$), if two of them are used as conditions and the remaining one as the conclusion, then they can form ___ correct propositions.

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