
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 vertical poles stand on sloped ground. The bottoms of the poles are 20 feet apart. One pole is 12 feet tall, and the other is 30 feet tall. The ground slopes upward between the poles, starting from the shorter pole and rising linearly at a rate of 1 foot height increase every 4 feet horizontal. How long, in feet, is a wire stretched from the top of the shorter pole to the top of the taller pole?

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