
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
$(1)\sqrt{16}+\sqrt{{{({-3})}^2}}+\sqrt[3]{{27}}$；  
$(2)-{1^{2020}}+\sqrt{25}-\sqrt{{{({1-\sqrt{2}})}^2}}+\sqrt[3]{{-8}}-\sqrt{{{({-3})}^2}}$；  
$(3)\left\{{\begin{array}{l}{3x+y=3}\\{3x-2y=-6}\end{array}}\right.$；  
$(4)\left\{{\begin{array}{l}{\frac{x}{3}+\frac{{y+1}}{2}=3}\\{2x-3y=9}\end{array}}\right.$；  
$(5)\frac{{1-x}}{2}-1≤\frac{{2x-6}}{3}$；  
$(6)\left\{\begin{array}{l}{4({x+1})≤7x+10}\\{x-5＜\frac{{x-8}}{3}}\end{array}\right.$.

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