
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 poles are 30 feet and 90 feet high and are 150 feet apart. Find the height at which the lines joining the top of each pole to the foot of the opposite pole intersect.

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