
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
In a certain recreational game, the host presents two bags, A and B, each containing 10 balls of identical size and shape but different colors. Bag A contains 8 red balls and 2 white balls, while Bag B contains 9 yellow balls and 1 black ball. The game's rules are as follows: drawing a red ball from Bag A scores 4 points, while drawing a white ball scores -1 point. Drawing a yellow ball from Bag B scores 6 points, while drawing a black ball scores -2 points.

1. If a ball is drawn from Bag A, its color recorded, and then returned to the bag, find the probability that the total score from four consecutive draws is no less than 10 points.
2. Let X (in points) denote the total score obtained by drawing one ball from each of Bag A and Bag B. Determine the expected value of X.

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