
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
Five lanterns of the same size but different colors (red, orange, yellow, green, purple) are connected from top to bottom and hung together end to end. It is required that red and purple are adjacent, orange and green are not adjacent, and orange cannot be at the top. The number of different ways to hang the lanterns is ______.

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