
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 the graph of the function $y=(\frac{1}{5})^{x+1}+m$ does not pass through the first quadrant, then the range of values for the real number $m$ is \_\_\_\_\_\_.

(2) It is known that the function $f(x)=x^{2}+(1-k)x-k$ has exactly one zero in the interval $(2,3)$. Then the range of values for the real number $k$ is \_\_\_\_\_\_.

(3) Given two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ such that $|\overrightarrow{a}|=2$, $|\overrightarrow{b}|=1$, and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $60^{\circ}$. If the angle between the vector $2t\overrightarrow{a}+7\overrightarrow{b}$ and the vector $\overrightarrow{a}+t\overrightarrow{b}$ is obtuse, then the range of values for the real number $t$ is \_\_\_\_\_\_.

(4) It is known that the function $f(x)=\sin x\tan x$. Give the following conclusions:
   ({①}) The function $f(x)$ is an even function;
   ({②}) The function $f(x)$ is an increasing function on the interval $(-\frac{\pi}{2},0)$;
   ({③}) The smallest positive period of the function $f(x)$ is $2\pi$;
   ({④}) The graph of the function $f(x)$ is symmetrical about the line $x=\pi$.
   The serial numbers of the correct conclusions are \_\_\_\_\_\_.

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