
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 box contains $6$ ballpoint pens, of which $4$ are first-class and $2$ are second-class. Two pens are drawn from the box in succession. Calculate the probability of the following events:
1. Exactly one first-class pen is drawn;
2. A second-class pen is drawn.

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