
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 strong wind broke a lightning rod, causing its top to hit the ground 20 meters from the base of the rod. The rod was repaired, but it broke again under a strong wind 5 meters lower than before, and this time the top hit the ground 30 meters from the base.

What is the height of the rod? In both cases, the broken part of the rod did not separate completely from the rest of it.

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