
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 $\overrightarrow{AB}=\overrightarrow{a}$, $\overrightarrow{BC}=\overrightarrow{b}$, and $\overrightarrow{CA}=\overrightarrow{c}$.
(1) Find $3\overrightarrow{a}+\overrightarrow{b}$;
(2) Find the real numbers $m$ and $n$ that satisfy $\overrightarrow{a}=m\overrightarrow{b}+n\overrightarrow{c}$.

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