
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
People have long been exploring the numerical solution of high-degree equations. Newton gave a numerical solution method for high-degree algebraic equations in his book "Fluxions." This method for finding the roots of equations has been widely used in the scientific community. For example, to find an approximate solution to the equation $x^{3}+2x^{2}+3x+3=0$, first using the existence theorem of function zeros, let $f\left(x\right)=x^{3}+2x^{2}+3x+3$, $f\left(-2\right)=-3 \lt 0$, $f\left(-1\right)=1 \gt 0$, it is known that there exists a zero on $\left(-2,-1\right)$, take $x_{0}=-1$. Newton used the formula ${x}_{n}={x}_{n-1}-\frac{f({x}_{n-1})}{{f}′({x}_{n-1})}$ for iterative calculation, where $x_{n}$ is taken as an approximate solution to $f\left(x\right)=0$. After two iterations, the approximate solution obtained is ______; starting with the interval $\left(-2,-1\right)$, using the bisection method twice, taking the midpoint value of the last interval as the approximate solution to the equation, the approximate solution is ______.

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