
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
Given the letters in the word "MATHEMATICS", determine how many distinguishable rearrangements of these letters have all vowels first, followed by consonants, and the letter 'T' always at the end of the arrangement.

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