
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 board, 'MATHEMATICS' is spelled out with 11 magnets, one for each letter. 'M', 'A', 'T', 'H', 'E', 'M', 'A', 'T', 'I', 'C', 'S' are the letters used. If three vowels and two consonants fall off and are put away in a bag, and considering that the 'A's and 'T's are indistinguishable, count the number of distinct possible collections of letters that could be put into the bag.

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