
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 an isosceles triangle $ \triangle OAB $ where $ |OA| = |OB| = 2 $ and $ | \vec{OA} + \vec{OB}| \geq \frac { \sqrt {3}}{3} | \vec{AB}| $, the range of the value of $ \vec{OA} \cdot \vec{OB} $ is \_\_\_\_\_.

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