
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
There is a pack of 27 distinct cards, and each card has three values on it. The first value is a shape from  $\{\Delta,\square,\odot\}$ ; the second value is a letter from  $\{A,B,C\}$ ; and the third value is a number from  $\{1,2,3\}$ .
In how many ways can we choose an unordered set of 3 cards from the pack, so that no two of the chosen cards have two matching values.
For example we can chose  $\{\Delta A1,\Delta B2,\odot C3\}$ But we cannot choose   $\{\Delta A1,\square B2,\Delta C1\}$ 

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