
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
(1) Let vector $\vec{a} = (-1,3)$, and vector $\vec{b} = (2,x)$, if $\vec{a} \parallel \vec{b}$, then $x = \boxed{-6}$.

(2) Given $p: x < -3$ or $x > 1$, $q: x > a$, if $\neg p$ is a sufficient but not necessary condition for $\neg q$, then the range of values for $a$ is $\boxed{a \geqslant 1}$.

(3) If the function $f(x)=\frac{4x}{x+4}$ and $x_1=1$, $x_{n+1}=f(x_n)$, then $x_{2017} = \boxed{\frac{1}{505}}$.

(4) Consider the following propositions:  
① The function $y=\sin \left(\frac{5\pi}{2} - 2x\right)$ is an even function;  
② The equation $x=\frac{\pi}{8}$ is an equation of a symmetry axis of the graph of the function $y=\sin \left(2x + \frac{5\pi}{4}\right)$;  
③ If $\alpha$ and $\beta$ are angles in the first quadrant, and $\alpha > \beta$, then $\sin \alpha > \sin \beta$;  
④ Let $x_1$ and $x_2$ be the roots of the equation $|\log_a x| = k$ ($a > 0$, $a \neq 1$, $k > 0$), then $x_1x_2=1$;  
Among these, the correct propositions are $\boxed{①②④}$.

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