
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:
$(1)$ The function $y=\sin ( \frac {5π}{2}-2x)$ is an even function;
$(2)$ The equation $x= \frac {π}{8}$ is a symmetry axis equation of the graph of the function $y=\sin (2x+ \frac {5π}{4})$;
$(3)$ If $α$ and $β$ are angles in the first quadrant and $α > β$, then $\sin α > \sin β$;
$(4)$ Let $x_{1}$ and $x_{2}$ be the two roots of the equation $|{\log _{a}x}|=k(a > 0,a\neq 1,k > 0)$ with respect to $x$, then $x_{1}x_{2}=1$;
Find the sequence number(s) of the correct proposition(s). (Fill in the sequence numbers of all correct propositions)

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