
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
Katrine has a bag containing 4 buttons with distinct letters M, P, F, G on them (one letter per button).  She picks buttons randomly, one at a time, without replacement, until she picks the button with letter G.  What is the probability that she has at least three picks and her third pick is the button with letter M? 


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