
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

a) How many possible pairs of keys can be formed with 10 distinct keys?

b) How many copies of each key does Fernando need to have to form all possible pairs of keys?

c) What is the minimum number of drawers Fernando needs to open to ensure he has possession of all 10 different keys to open the gate of his house?

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