
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 has exactly 6 red buttons and 10 blue buttons. Carla then removes the same number of red buttons as blue buttons from Jar C and places them in an empty Jar D. Jar C now has $\frac{3}{4}$ of its original number of buttons. If Carla were to randomly choose a button from Jar C and a button from Jar D, what is the probability that the two chosen buttons will both be blue?

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