
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
A plane intersects the edges \(AB\), \(BC\), and \(CD\) of a regular tetrahedron \(ABCD\) at points \(K\), \(L\), and \(M\), respectively, such that \(AK = 2KB\), \(BL = CL\), and \(CM = 2MD\). In what ratio does the plane divide the surface area of the tetrahedron?

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