
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
How many five-digit numbers can be formed

a) with all identical digits,

b) with two different digits,

c) with three different digits,

d) with four different digits,

e) with five different digits?

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