
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
Xiao Wang created a WeChat group consisting of himself, A, B, and C, and sent red envelopes to the group. Each time he sent one red envelope (excluding himself), assuming that A, B, and C have the same probability of receiving the red envelope.

$(1)$ If Xiao Wang sends 2 red envelopes, find the probability that A receives exactly 1 red envelope.

$(2)$ If Xiao Wang sends 3 red envelopes, with the first and second envelopes containing 5 yuan each, and the third envelope containing 10 yuan, find the probability that the total amount of money B receives from all the red envelopes is at least 10 yuan.

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