
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 pyramid $ABCD$, the area of the face $ABC$ is four times the area of the face $ABD$. Point $M$ is taken on the edge $CD$ such that $CM: MD = 2$. Through point $M$, planes parallel to the faces $ABC$ and $ABD$ are drawn. Find the ratio of the areas of the resulting sections.

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