
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 triangle, the sides are known to be \( AB = 15 \), \( BC = 13 \), and \( AC = 14 \). From point \( C \), a perpendicular is drawn to side \( AC \) and intersects with the extension of side \( AB \) at point \( K \). Find \( BK \) and \( CK \).

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