
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 there are five houses painted a different bright color, with the green house before the violet house, the indigo house before the teal house, the indigo house not adjacent to the teal house, and the green house not adjacent to the violet house, determine the number of possible orderings of the colored houses.

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