
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 a plane, three vectors are given as $\overrightarrow {a}=(3,2)$, $\overrightarrow {b}=(-1,2)$, $\overrightarrow {c}=(4,1)$.
(1) Find $3\overrightarrow {a}+\overrightarrow {b}-2\overrightarrow {c}$.
(2) Find the real numbers $m$ and $n$ that satisfy $\overrightarrow {a}=m\overrightarrow {b}+n\overrightarrow {c}$.
(3) If $\left(\overrightarrow {a}+k\overrightarrow {c}\right) \parallel \left(2\overrightarrow {b}-\overrightarrow {a}\right)$, find the real number $k$.

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