
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 all real numbers $a$ that satisfy the following conditions: For every infinite sequence of distinct positive integers $a_{1}, a_{2}, \cdots, a_{n}, \cdots$ such that $a_{n} \leqslant a n$ for every positive integer $n$, the sequence contains infinitely many terms for which the sum of the digits in base 4038 is not divisible by 2019.

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