
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 \\(\vec{a}=(x,2)\\), \\(\vec{b}=(1,y)\\), \\(\vec{c}=(2,-6)\\), given that \\(\vec{a} \perp \vec{c}\\), and \\(\vec{b} \parallel \vec{c}\\), then the magnitude of \\(\vec{a}+ \vec{b}\\) is __________.

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