
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
Scientists have identified 15 habitable planets through new telescopes. Of these, 7 are categorized as "Blue-like" thanks to their abundant water resources, and the remaining 8 are "Orange-like" due to their scarce water but mineral-rich surfaces. Assume settling a Blue-like planet requires 3 units of colonization effort, while Orange-like planets require 2 units each. If a total of 21 units of colonization is available, how many distinct ways can these planets be occupied, given that each planet is unique?

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