
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
On a notice board, MATHEMATICSH is spelled out with $12$ cards, one letter per card. Three vowels and three consonants fall off and are put away in a box. If the T's, M's, A's, and H's are indistinguishable, how many distinct possible collections of letters could be put in the box?

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