
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
Jar C initially contains 6 red buttons and 12 green buttons. Michelle removes the same number of red buttons as green buttons from Jar C and places them into an empty Jar D. After the removal, Jar C is left with $\frac{3}{4}$ of its initial button count. If Michelle were to randomly choose a button from Jar C and a button from Jar D, what is the probability that both chosen buttons are green? Express your answer as a common fraction.

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