
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
From vertex \( B \) of parallelogram \( ABCD \), the perpendicular heights \( BK \) and \( BH \) are drawn. The segments \( KH = a \) and \( BD = b \) are known. Find the distance from point \( B \) to the orthocenter of triangle \( BKH \).

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