
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
MATHCOUNTS is again spelled out with 10 magnets, but now the N's are also identical to each other, making both T's and N's indistinguishable. Three vowels and two consonants fall off and are put away in a bag. How many distinct possible collections of letters could be put in the bag?

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