
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 $m=\int_{0}^{\frac{\pi}{2}}{\sqrt{2}\sin \left( x+\frac{\pi}{4} \right)dx}$, then the coefficient of the term containing $x$ in the expansion of the binomial $\left( \sqrt{x}-\frac{m}{\sqrt{x}} \right)^{6}$ is ______.

(2) Given that $f(x)$ is an odd function defined on $\mathbb{R}$, and $f(x+4)=f(x)$, when $0 < x < 2$, $f(x)={2}^{x}-1$, then $f(-21)+f(16)=$ ______.

(3) The school plans to arrange for six teachers to be on duty from May 1st to May 3rd, requiring each person to be on duty for one day, with two people arranged each day. If among the six teachers, Teacher Wang cannot be on duty on May 2nd, and Teacher Li cannot be on duty on May 3rd, then the probability of meeting this requirement is ______.

(4) For the function $f(x)=\begin{cases}x^{2}+2x-1, & x\geqslant a \\ -x^{2}+2x-1, & x < a\end{cases}$, for any real number $b$, the function $y=f(x)-b$ has at most one zero point, then the range of values for the real number $a$ is ______.

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