
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
Alex writes the digits $1$ to $6$ repeatedly from left to right, forming a list of $12,000$ digits starting as: $123456123456\ldots.$ He then erases every fifth digit from his list (i.e., $5^{th}, 10^{th}, 15^{th}, \ldots$ digits). After this, he erases every seventh digit from the new sequence (e.g., $7^{th}, 14^{th}, $21^{st}$, \ldots$). What is the sum of the three digits in positions $3031, 3032, 3033$ of the final sequence?

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