
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
In the plane, three vectors are given: $\overrightarrow{a}=(3,2)$, $\overrightarrow{b}=(-1,2)$, $\overrightarrow{c}=(4,1)$.

(1) Find $3\overrightarrow{a} + \overrightarrow{b} - 2\overrightarrow{c}$.

(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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