
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
In a box containing $6$ fountain pens, there are $3$ first-class pens, $2$ second-class pens, and $1$ third-class pen. If two pens are randomly drawn from the box:
1. Find the probability of drawing exactly $1$ first-class pen.
2. Find the probability of not drawing any third-class pen.

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