
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
Walking down the street, Ralph passes five houses in a row, each painted a different color: orange, red, blue, yellow, and green. Given that he passed the orange house before the red house, the blue house before the yellow house, the green house is exactly two houses away from the blue house, and the blue house was not next to the yellow house, determine the number of possible orderings of the colored houses.

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