
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
Reading Material:  
Factorization: $x^{2}+2x-3$  
Solution: The original expression $=x^{2}+2x+1-1-3=(x^{2}+2x+1)-4=(x+1)^{2}-4=(x+1+2)(x+1-2)=(x+3)(x-1)$  
This method captures the characteristics of the quadratic and linear terms, then adds a term to make these three terms a complete square. We call this method of factorization the "completing the square" method. Please carefully understand the characteristics of the completing the square method, and then try to use this method to solve the following problems:  
$(1)$ Factorize: $m^{2}-4mn+3n^{2}$;  
$(2)$ Regardless of the value of $m$, the algebraic expression $m^{2}-3m+2015$ always has a minimum value. Please try to use the completing the square method to find its minimum value.

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