
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
A wizard is preparing an invisibility elixir. He has access to four magical roots and six enchanted minerals. However, due to the volatile nature of the ingredients, one particular mineral is incompatible with three of the roots. There are no other restrictions on the combinations. How many valid combinations can the wizard use to create his elixir?

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