
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, of which there are $2$ red balls, $2$ yellow balls, and $2$ blue balls. Each time, one ball is drawn from the box (with replacement, so each ball has an equal chance of being drawn). This process 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 the balls drawn in all three draws is the same". Then, $P(B|A)=$ ___.

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