
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 \( x \in \mathbb{R} \), and the plane vectors \( \vec{a} = (2, 1) \), \( \vec{b} = (-1, x) \), \( \vec{c} = (2, -4) \). If \( \vec{b} \parallel \vec{c} \), calculate the magnitude of the vector \( \vec{a} + \vec{b} \).

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