
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
Humanity discovers a new solar system with 20 planets, of which 8 are Earth-like and 12 are Mars-like. Colonizing an Earth-like planet requires 3 units of resources, while a Mars-like planet requires only 1 unit. If humanity has 18 units of resources available for colonization, how many different combinations of planets can be occupied, assuming all planets are distinct?

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