
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 shooters, A, B, and C, participate in a shooting competition. It is known that their probabilities of hitting the target are 0.7, 0.8, and 0.5, respectively. Now, each of them shoots at the target once in turn. Let the number of times the target is hit be denoted as $X$.
(1) Find the probability distribution of the random variable $X$.
(2) Find the expected value of the random variable $X$.

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