
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
Point $G$ is the centroid of $\triangle ABC$, $\overrightarrow{AG}=λ \overrightarrow{AB}+μ \overrightarrow{AC}$, where $(λ,μ∈R)$, if $\angle A=120^{\circ}$, $\overrightarrow{AB}\cdot \overrightarrow{AC}=-2$, then the minimum value of $|\overrightarrow{AG}|$ is $\_\_\_\_\_\_\_\_\ $

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