
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
Define a number as special-prime-looking if it is composite but not divisible by $2, 7,$ or $11$. The three smallest special-prime-looking numbers are $15, 21$, and $33$. There are $303$ prime numbers less than $2000$. How many special-prime-looking numbers are there less than $2000$?
- $(\mathrm {A}) \ 460$
- $(\mathrm {B}) \ 478$
- $(\mathrm {C})\ 490$
- $(\mathrm {D}) \ 504$
- $(\mathrm {E})\ 520$

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