
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 propositions:
(1) There exists a real number $α$, such that $sin⁡αcos⁡α=1$;
(2) The function $y=sin⁡(3π2+x)$ is an even function;
(3) The line $x=π8$ is a symmetry axis of the function $y=sin⁡(2x+5π4)$;
(4) If $α$ and $β$ are angles in the first quadrant, and $α>β$, then $sin⁡α>sin⁡β$.
Determine the sequence number(s) of the correct proposition(s).

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