
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 Carla passed five houses in a row, each painted a different color, with the green house before the purple house, the blue house before the pink house, the pink house not adjacent to the blue house, and the green house being either the first or last in the row, determine the number of different orderings of colored houses.

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