
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
"We call the polynomials $a^{2}+2ab+b^{2}$ and $a^{2}-2ab+b^{2}$ as perfect square trinomials." If a polynomial is not a perfect square trinomial, we often perform the following transformation: first add a suitable term to make a perfect square trinomial appear in the expression, then subtract this term so that the value of the entire expression remains unchanged. This method is called the method of completing the square. Completing the square is an important mathematical method for solving problems. It can not only factorize a seemingly indivisible polynomial, but also solve some problems related to non-negative numbers or find the maximum and minimum values of algebraic expressions. For example: Factorize $x^{2}+2x-3=(x^{2}+2x+1)-3-1=(x+1)^{2}-4=(x+1+2)(x+1-2)=(x+3)(x-1)$. Find the minimum value of the algebraic expression $2x^{2}+4x-6$: $2x^{2}+4x-6=2(x^{2}+2x)-6=2(x^{2}+2x+1)-6-2=2(x+1)^{2}-8$. Since $(x+1)^{2}\geqslant 0$, therefore $2(x+1)^{2}-8\geqslant -8$, so when $x=-1$, $2x^{2}+4x-6$ has the minimum value, which is $-8$. According to the material, use the method of completing the square to solve the following problems: (1) Factorize $x^{2}-4x-5$; (2) For what value of $x$ does the polynomial $-2x^{2}-4x+3$ have the maximum value? And find this maximum value.

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