
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
Given points $A(-2,4)$, $B(3,-1)$, and $C(-3,-4)$. Let $\overrightarrow{AB}=a$, $\overrightarrow{BC}=b$, $\overrightarrow{CA}=c$, and $\overrightarrow{CM}=3c$, $\overrightarrow{CN}=-2b$.

(1) Find $3a+b-3c$;

(2) Find the real number values of $m$ and $n$ that satisfy $a=mb+nc$;

(3) Find the coordinates of points $M$ and $N$ and the coordinates of vector $\overrightarrow{MN}$.

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