
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 Jane Street, Ralph passed five houses in a row, each painted a different color. He passed the green house before the blue house, the violet house before the green house, and he passed the yellow house before the red house. The red house was not next to the blue house, and the violet house was never the first or last. Determine the number of possible orderings of the colored houses.

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