
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
What is the smallest number that is composed only of the digits 3 and 7 and such that both the number itself and the sum of its digits are divisible by 3 and 7? For example, 7733733 is divisible by 3 and 7, but the sum of its digits (33) is divisible by 3 but not by 7, so it cannot be the solution.

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