
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. Four drivers and four ticket sellers form four groups, each with one driver and one ticket seller. The number of different grouping schemes is \_\_\_\_\_\_.
2. Assume that the random variable $\xi$ follows a normal distribution $N(3,4)$. If $P(\xi > 2a-3)=P(\xi < a+2)$, the value of $a$ is \_\_\_\_\_\_.
3. The remainder when $S=C_{27}^{1} +C_{27}^{2} +…+C_{27}^{27}$ is divided by $9$ is \_\_\_\_\_\_.
4. If the proposition "$\exists x \in R, {x}^{2}+(a-1)x+1 < 0$" is false, the range of the real number $a$ is \_\_\_\_\_\_.

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