
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
Given proposition $q$: "$\exists x$ such that $-2 \lt x \lt 2$, $x^{2}-2x-a=0$".<br/>$(1)$ Proposition $p$: "$\exists x\in R$, $x^{2}+\left(a-1\right)x+4 \lt 0$", if at least one of propositions $p$ and $q$ is true, find the range of real number $a$.<br/>$(2)$ Proposition $p: 2a \lt x \lt a+1$, if $p$ is a sufficient but not necessary condition for $q$, find the range of real number $a$.

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