
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 large magnetic board, the word MATHEMATICEONS is spelled out using $13$ magnets, one magnet per letter. Three vowels and five consonants fall off and are put into a bag. The E's, C's, and N's, and the original T's, M's, and A's are indistinguishable. How many distinct collections of letters could be put into the bag?

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