
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
Answer the following questions as required:
1. Factorize: $m^{2}(n-3)+4\left(3-n\right)$;
2. Factorize: $\left(p-3\right)\left(p-1\right)+1$;
3. Simplify first, then find the value: $(\frac{2x+1}{x+1}+x-1)÷\frac{x+2}{x^2+2x+1}$, where $x$ satisfies $x^2+x+\frac{1}{4}=0$.

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