
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 a non-right triangle $\triangle ABC$ with angles $A$, $B$, $C$ and the lengths of the opposite sides $a$, $b$, $c$ respectively, which of the following statements are correct (write down all the correct statement numbers).

① "sinA > sinB" is a necessary and sufficient condition for "a > b";  
② "cosA < cosB" is a necessary and sufficient condition for "a > b";  
③ "tanA > tanB" is a necessary and sufficient condition for "a > b";  
④ "sin2A > sin2B" is a necessary and sufficient condition for "a > b";  
⑤ "cos2A < cos2B" is a necessary and sufficient condition for "a > b".

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