
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
From the first machine, 200 parts were submitted for assembly, of which 190 are standard; from the second machine - 300 parts, of which 280 are standard. Find the probability of event $A$, which consists of randomly selecting a standard part, and the conditional probabilities of this event relative to events $B$ and $\bar{B}$, where event $B$ consists of the part being manufactured on the first machine.

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