
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
We place a coin in one of three identical boxes and then put these three boxes into two drawers such that each drawer contains at least one box. What is the probability that if someone randomly selects a drawer and then takes a box out from that drawer, they will find the coin in that box,

a) if the box containing the coin is alone in one drawer?

b) if the box containing the coin is in a drawer with one other box?

c) if the 3 boxes are randomly placed into the two drawers without knowing which box contains the coin?

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