
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
$(1)$ Calculate ${2}^{-1}+|-\frac{1}{4}|-202{3}^{0}$;<br/>$(2)$ Simplify $2x\cdot x^{2}-(-x^{4})^{2}\div x^{5}$;<br/>$(3)$ Factorize $x^{3}-6x^{2}+9x$;<br/>$(4)$ Simplify first, then find the value: $\left(2x+1\right)-2\left(x-2\right)\left(x+2\right)$, where $x=-\frac{1}{2}$.

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