
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) $1101011_{(2)}=$ _______${}_{(10)}$.

(2) Given the variance of the data $a_{1}$, $a_{2}$, $a_{3}$, …, $a_{n}$ is $9$, then the standard deviation of the data $2a_{1}+5$, $2a_{2}+5$, $2a_{3}+5$, …, $2a_{n}+5$ is _______.

(3) Select a number denoted as $a$ from the set $\left\{ \frac{1}{2} , \frac{1}{3} ,2,3\right\}$, and a number denoted as $b$ from the set $\{-2,-1,1,2\}$, then the probability that the graph of the function $y=a^{x}+b$ passes through the third quadrant is _______.

(4) Consider the following statements:  
① The values of the trigonometric functions of angles with the same terminal side are equal;  
② The values of the trigonometric functions of angles with different terminal sides are not equal;  
③ If $\sin \alpha > 0$, then $\alpha$ is an angle in the first or second quadrant;  
④ If $\sin \alpha=\sin \beta$, then $\alpha=2k\pi+\beta$, $k\in Z$;  
⑤ If $\alpha$ is an angle in the second quadrant, then $\frac{\alpha}{2}$ is an angle in the first quadrant.  

The correct statement(s) is/are _______.

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