
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 three vectors in the plane: $\overrightarrow{a}=(3,2)$, $\overrightarrow{b}=(-1,2)$, $\overrightarrow{c}=(4,1)$  
(Ⅰ) If $(\overrightarrow{a}+k\overrightarrow{c})\parallel(2\overrightarrow{b}-\overrightarrow{a})$, find the value of the real number $k$;  
(Ⅱ) Let $\overrightarrow{d}=(x,y)$, and it satisfies $(\overrightarrow{a}+\overrightarrow{b})\perp(\overrightarrow{d}-\overrightarrow{c})$, $|\overrightarrow{d}-\overrightarrow{c}|= \sqrt{5}$, find $\overrightarrow{d}$．

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