
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,1)\\), \\(\overrightarrow{b}=(2,y)\\), \\(\overrightarrow{c}=(-2,2)\\), given that \\(\overrightarrow{a} \perp \overrightarrow{c}\\) and \\(\overrightarrow{b} \parallel \overrightarrow{c}\\), find the magnitude of \\(\overrightarrow{a}+\overrightarrow{b}\\).

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