
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 "Fluxional Method" - Newton's method. 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 ${x}_{n}={x}_{n-1}-\frac{f({x}_{n-1})}{{f}′({x}_{n-1})}$ to iteratively find the 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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