
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

Two cones have a common base and are located on opposite sides of it. The radius of the base is \( r \), the height of one cone is \( h \), and the height of the other cone is \( H \) (\( h \leq H \)). Find the maximum distance between two generatrices of these cones.

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