
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
How many of the following conclusions are correct in △ABC?
① $A > B \Leftrightarrow \cos A < \cos B$; ② $A > B \Leftrightarrow \sin A > \sin B$; ③ $A > B \Leftrightarrow \cos(2A) < \cos(2B)$.

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