
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) In a bag, there are red balls (2 pieces), white balls (3 pieces), and yellow balls (1 piece) of the same size and shape. If a person draws balls one by one without replacement and the first draw is a red ball, the probability of drawing a white ball on the second draw is ______.

(2) Given a discrete random variable $\xi$ that follows a normal distribution $N～(2,1)$, and $P(\xi < 3)=0.968$, then $P(1 < \xi < 3)=$ ______.

(3) Let ${x}_1,{x}_2,{x}_3,{x}_4 \in \{-1,0,2\}$. The number of ordered arrays $\{{x}_1,{x}_2,{x}_3,{x}_4\}$ that satisfy $2\leqslant |{x}_1|+|{x}_2|+|{x}_3|+|{x}_4|\leqslant 4$ is ______.

(4) Given ${a}\in \mathbb{R}$, the function ${f}\left( {x} \right)=\left| {x}+\dfrac{4}{{x}}-{a} \right|+{a}$ has a maximum value of $5$ in the interval $[1,4]$. The range of values for $a$ is ______.

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