
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
There are four letters \(A, B, C, D\) and three mailboxes labeled 1, 2, and 3. If the four letters can be randomly placed into any of the mailboxes until all letters are placed, find:
(1) The probability that mailbox 3 contains exactly 1 letter.
(2) The probability that letter \(A\) is placed into either mailbox 1 or mailbox 2.

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