
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 crafting a magical elixir. For this, he requires one of four magical herbs and one of six enchanted gems. However, one of the gems cannot be used with three of the herbs. Additionally, another gem can only be used if it is paired with one specific herb. How many valid combinations can the wizard use to prepare his elixir?

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