
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 that Ralph passed the orange house before the red house, the blue house before the yellow house, the blue house not next to the yellow house, and the green house not next to the blue house, determine the number of orderings of the colored houses.

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