
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
Three vectors $$\overrightarrow {a}=(3, 2), \overrightarrow {b}=(-1, 2), \overrightarrow {c}=(4, 1)$$ are given in the plane. 
(1) Find the real numbers $m$ and $n$ that satisfy $$\overrightarrow {a}=m \overrightarrow {b}+n \overrightarrow {c}$$.
(2) Let $$\overrightarrow {d}=(x, y)$$ be a vector such that $$(\overrightarrow {d}-\overrightarrow {c}) \parallel (\overrightarrow {a}+\overrightarrow {b})$$ and $$|\overrightarrow {d}-\overrightarrow {c}|=1$$. Find $$\overrightarrow {d}$$.

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