
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 two planar vectors $ \overrightarrow{a} $ and $ \overrightarrow{b} $ with an angle of $60^{\circ}$ between them, where $ \overrightarrow{a}=(2,0) $ and the magnitude of $ \overrightarrow{b} $ is 1, find the magnitude of $ \overrightarrow{a}+2 \overrightarrow{b} $.

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