
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
Calculate:<br/>$(1)\sqrt{50}+\frac{2}{\sqrt{2}+1}-4\sqrt{\frac{1}{2}}+2(\sqrt{2}-1)^{0}$;<br/>$(2)\left(x-5\right)\left(x+2\right)=8$;<br/>$(3)\left(x+3\right)\left(x-2\right)=2x+6$;<br/>$(4)\frac{3}{2}x^{2}+4x-1=0$.

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