
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 problems:  
$(1)$ Calculate: $\left(x-2y\right)^{2}-x\left(x+3y\right)-4y^{2}$;  
$(2)$ Factorize: $3x^{2}-6xy+3y^{2}-27m^{2}$;  
$(3)$ Calculate: $(3\sqrt{12}-2\sqrt{\frac{1}{3}}+\sqrt{48})÷2\sqrt{3}$;  
$(4)$ Calculate: $|x-3|+|3x+2| \lt 15$.

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