
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
A bag contains $6$ balls of the same size, which are either black or white. It is known that the probability of drawing at least $1$ white ball when drawing $2$ balls from the bag is $\frac{4}{5}$. Find the number of white balls in the bag and the mathematical expectation of the number $X$ of white balls drawn when drawing $2$ balls from the bag.

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