
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 a magic elixir. He has four different flowers and six different gems to choose from. However, one of the gems is incompatible with three of the flowers. How many valid combinations of flowers and gems can the wizard use to prepare his elixir?

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