
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 has discovered a new solar system with 15 planets, of which 7 are Earth-like and 8 are Mars-like. Each Earth-like planet requires 3 units of colonization, while Mars-like planets require 1 unit. If humanity has 21 total units of colonization available, how many different combinations of planets can they occupy assuming each planet is distinct?

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