
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
Given two poles 30'' and 60'' high are 120'' apart, calculate the height of the intersection of the lines joining the top of each pole to the foot of the opposite pole.

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