
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
After discovering a new group of planets, scientists identify 12 habitable planets. Out of these 12, 6 are considered "Earth-like" (requiring 3 units of colonization each due to their complexity and resource abundance) and the remaining 6 are "Mars-like" (requiring 1 unit of colonization each as they are less resourceful). Given that humanity can mobilize 15 units of colonization in total, how many different configurations of planets can be occupied, considering that all planets are distinct?

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