
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 Maple Lane, Sonia passed five houses, with each house uniquely painted and patterned. The colors are ordered as follows: red stripes, green dots, blue waves, yellow zigzags, and pink spirals. Additionally, blue waves were not adjacent to pink spirals, nor were blue waves adjacent to yellow zigzags. Determine the number of valid orderings of the colored and patterned houses.

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