
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 have 30 piggy banks, each with a unique key that does not open any of the other piggy banks. Someone randomly places the keys into the locked piggy banks, one per piggy bank. We then break open two piggy banks. What is the probability that we can open all the remaining piggy banks without breaking any more piggy banks?

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