
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
1. Two identical fair coins are tossed simultaneously. The random variable $\xi=1$ represents the outcome where at least one coin shows heads, and $\xi=0$ represents the outcome where no coins show heads. Find $E[\xi]$.

2. In a basketball game, with 0.1 seconds remaining, Team A is awarded two free throws while trailing with a score of 100:101. The statistical data for the free-throw shooter shows: the probability of making the first shot is 0.6. If the first shot is made, the probability of making the second shot is 0.8; if the first shot is missed, the probability of making the second shot is 0.7. Find the expected value of the points scored by Team A after the free throws.

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