
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
A device used to determine the diameter \( D \) of a large part (\( D > 2 \) m) indicates the height \( H \) of the segment when the constant distance between the centers of the supporting balls of the device is \( 2L \). You are required to express the formula that relates the desired diameter \( D \) of the part to the measured height \( H \) of its segment, given constants \( L \) and \( d \), where \( d \) is the diameter of each supporting ball.

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