
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
Find the number of counterexamples to the statement that a number $N$ with the sum of its digits equal to $5$ and none of its digits being $0$ must be prime.
A) 4
B) 5
C) 6
D) 7
E) 8

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