
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 the planar vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ with an angle of $\frac {π}{3}$ between them, and satisfying $| \overrightarrow {a}|=2$ and $| \overrightarrow {b}|=1$, find the values of $\overrightarrow {a}\cdot \overrightarrow {b}$ and $| \overrightarrow {a}+2 \overrightarrow {b}|$.

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