
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 A initially contains five red buttons and ten blue buttons. Carla removes the same number of red and blue buttons from Jar A and places them in an empty Jar B. After the removal, Jar A has $\frac{3}{5}$ of its original number of buttons. If Carla randomly chooses one button from each jar, what is the probability that both selected buttons are red?

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