
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 finds another habitable system with 12 planets, out of which 7 are "Venus-like" and 5 are "Jupiter-like". "Venus-like" planets require 3 units of colonization due to harsher climates, while "Jupiter-like" planets require only 1 unit. Given 15 total units of colonization effort available, how many different combinations of planets can be occupied if all planets are distinct?

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