
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
Let $x, y \in \mathbb{R}$, and vectors $\overrightarrow{a}=(x,2)$, $\overrightarrow{b}=(4,y)$, $\overrightarrow{c}=(1,-2)$, with $\overrightarrow{a} \perp \overrightarrow{c}$ and $\overrightarrow{b} \parallel \overrightarrow{c}$.  
(Ⅰ) Find the values of $x$ and $y$;  
(Ⅱ) Find the value of $|\overrightarrow{a}+ \overrightarrow{b}|$.

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