
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

Claudia likes to play with numbers that have two or more digits. She chooses one of these numbers, multiplies its digits, and if the product has more than one digit, she adds them up. She calls the final result the transformed number. For example, the transformed number of 187 is 11, since $1 \times 8 \times 7=56$ and $5+6=11$; the transformed number of 23 is 6, since $2 \times 3=6$.

a) What is the transformed number of 79?

b) What are the two-digit numbers whose transformed number is 3?

c) How many three-digit numbers have a transformed number of 0?

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