
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
On each median of a triangle, a point is taken that divides the median in the ratio \(1:3\), starting from the vertex. By how much is the area of the triangle with vertices at these points smaller than the area of the original triangle?

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