
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
Dominic randomly picks between two words MATHEMATICS and MEMES, each with an equal chance of being chosen. From his chosen word, he then randomly draws one letter, with the probability of each letter being drawn directly proportional to the frequency of its occurrence in the word. Given that Dominic drew an M, what is the probability that he picked MEMES?

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