
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 contains exactly six red buttons and ten blue buttons. Carla removes three red buttons and five blue buttons from Jar C and places them in an empty Jar D. Jar C now holds half of its initial total number of buttons. If Carla now were to randomly choose a button from Jar C and a button from Jar D, what is the probability that both chosen buttons will be blue?

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