
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
Let  $n\in \mathbb{Z}_{> 0}$ . The  set  $S$  contains all positive integers written in decimal form that simultaneously satisfy the following conditions:
[list=1][*] each element of  $S$  has exactly  $n$  digits;
[*] each element of  $S$  is divisible by  $3$ ;
[*] each element of  $S$  has all its digits from the set  $\{3,5,7,9\}$  [/list]
Find  $\mid S\mid$ 

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