
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
In the diagram, lines $AB\parallel CD\parallel EF$. Line segments $AB$ and $CD$ are not of equal length. Length of $AB = 180$ cm and length of $CD = 120$ cm. If $h_{AB} = 1.5h_{CD}$ where $h_{AB}$ and $h_{CD}$ are the vertical distances from $AB$ and $CD$ to a line parallel to them through point $E$, find the length of $EF$.

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