
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
In the right trapezoid $ABCD$, $\angle A=90^{\circ}$, $\angle B=30^{\circ}$, $AB=2 \sqrt{3}$, $BC=2$. Point $E$ is on the line segment $CD$. If $\overrightarrow{AE}=\overrightarrow{AD}+\mu \overrightarrow{AB}$, then the range of values for $\mu$ is ______.

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