
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
Given a box containing $6$ balls, with $2$ red balls, $2$ yellow balls, and $2$ blue balls each, and the process of drawing a ball with replacement is repeated three times. Let event $A$ be "the color of the ball drawn in the first draw is the same as the color of the ball drawn in the second draw", and event $B$ be "the color of all three drawn balls is the same". Calculate the conditional probability $P(B|A)$.

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