
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 the side \(AC\) of triangle \(ABC\), points \(E\) and \(K\) are taken such that \(E\) lies between \(A\) and \(K\), and \(AE:EK:KC = 3:5:4\). Median \(AD\) intersects segments \(BE\) and \(BK\) at points \(L\) and \(M\) respectively. Find the ratio of the areas of triangles \(BLM\) and \(ABC\). The answer is \(\frac{1}{5}\).

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