
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 that $| \overrightarrow{OA}|=| \overrightarrow{OB}|=1,| \overrightarrow{AB}|= \sqrt {3}$, find the value of $\overrightarrow{OA}\cdot \overrightarrow{OB}$ and $| \overrightarrow{OA}+ \overrightarrow{OB}|$.

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