
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
Solve the following quadratic inequalities:<br/>$(1)\frac{1}{2}x^{2}-4x+6 \lt 0$;<br/>$(2)4x^{2}-4x+1\geqslant 0$;<br/>$(3)2x^{2}-x-1\leqslant 0$;<br/>$(4)3\left(x-2\right)\left(x+2\right)-4\left(x+1\right)^{2}+1 \lt 0$.

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