
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
It is known that: "In an equilateral triangle $ABC$, if $D$ is the midpoint of $BC$, and $G$ is the center of the circumscribed circle of $\triangle ABC$, then $\dfrac{AG}{GD}=2$." If we extend this conclusion to space, we have the conclusion: "In a tetrahedron $ABCD$ with all six edges equal, if $M$ is the intersection point of the medians of $\triangle BCD$, and $O$ is the center of the circumscribed sphere of the tetrahedron $ABCD$, then $\dfrac{AO}{OM}=$ ______.

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