
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 randomly placed the keys of thirty piggy banks into the closed piggy banks, one key per piggy bank.

We break open one piggy bank. What is the probability that after this we can open all piggy banks without having to break another one?

What is the probability if we break open two piggy banks at the beginning?

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