
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
The triangle \(ABC\) has three sides: \(a, b, c\). The triangle, where \(b > c\), is divided into two equal-area parts by the line \(HK\) which is perpendicular to the base \(BC\). What is the distance of the foot of the perpendicular \(HK\) from point \(C\)?

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