
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 mixing a magical concoction. To prepare this, she needs to select one of four herbs and one of six crystals. However, one of the crystals is incompatible with one of the herbs, and another crystal is incompatible with two different herbs. How many valid combinations can the wizard use to prepare her concoction?

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