
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 triangle \( ABC \), the sides \( AB \), \( AC \), and \( BC \) are 5, 6, and 7 respectively. On the median \( AM \), segment \( AK \) is set to be 2. Find the ratio of the areas of triangles \( ABK \) and \( ACK \). Provide the answer as \(\frac{S_{ABK}}{S_{ACK}}\).

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