
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
Three people, labeled as A, B, and C, independently attempt to decode the same cipher. The probabilities that each person successfully decodes the cipher are 0.4, 0.35, and 0.3, respectively. Let the random variable $X$ represent the number of people who successfully decode the cipher. Find:  
(1) The probability that exactly two people decode the cipher, $P(X=2)$;  
(2) The probability that the cipher is decoded by at least one person, $P(X\geq1)$.

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