
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 creating a magical elixir. To complete the elixir, he must select one of four magical herbs and one of six enchanted crystals. However, one of the crystals is incompatible with three of the herbs. How many valid combinations can the wizard choose from to successfully create his elixir?

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