
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. Given that $i$ is the imaginary unit and the complex number $z=(2+i)^{2}$, find the conjugate of $z$, denoted as $\overline{z}$.
2. The circle given by the equation $x^{2}+y^{2}=1$ undergoes a transformation defined by the system of equations $\begin{cases} x'=2x \\ y'=3y \end{cases}$. Determine the equation of the resulting curve.
3. Find the equation of the tangent line to the curve $y=\ln x$ at the point where $x=e$.
4. Given proposition $p$: "$\forall x\in[1,2], x^{2}-a\geqslant 0$" and proposition $q$: "$\exists x_{0}\in R, x_{0}^{2}+2ax_{0}+2-a=0$", if the proposition "$p$ and $q$" is true, find the range of values for the real number $a$.

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