
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) If one of the asymptotes of the hyperbola $\dfrac{x^{2}}{m^{2}}-y^{2}=1$ $(m > 0)$ is $x+\sqrt{3}y=0$, then $m=$ ______.

(2) Given a sequence $\{a_{n}\}$ satisfies $a_{1}+a_{3}=\dfrac{5}{8}, a_{n+1}=2a_{n}$, and the sum of the first $n$ terms is $S_{n}$, then the value of $S_{n}-2a_{n}$ is ______.

(3) In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $\dfrac{4\sqrt{3}}{3}S_{\triangle ABC}=b^{2}+c^{2}-a^{2}$, then the angle $A=$ ______ (in radians).

(4) Consider the following propositions:  
① The converse of the proposition "In $\triangle ABC$, if $A=B$, then $\sin A=\sin B$" is true;  
② If a moving point $P$ has a constant sum of distances to two fixed points $F_{1}(-4,0)$ and $F_{2}(4,0)$ equal to $8$, then the trajectory of point $P$ is the line segment $F_{1}F_{2}$;  
③ If $p∧q$ is a false proposition, then both $p$ and $q$ are false propositions;  
④ For $x\in R$, " $x^{2}-3x > 0$" is a necessary but not sufficient condition for "$x > 4$";  
⑤ If the real numbers $1$, $m$, $9$ form a geometric sequence, then the eccentricity of the conic section $\dfrac{x^{2}}{m}+y^{2}=1$ is $\dfrac{\sqrt{6}}{3}$;  
Among these, the correct propositions are ______.

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