
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
If the sum of the digits of a natural number \( a \) is equal to 7, then \( a \) is called a "lucky number". Arrange all the "lucky numbers" in increasing order as \( a_{1}, a_{2}, a_{3}, \cdots \). If \( a_{n}=2005 \), what is \( a_{5n} \)?

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