
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) Find all three-digit numbers that are equal to the sum of the factorials of their digits.

b) Find all integers that are equal to the sum of the squares of their digits.

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