
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
Write the five-digit number "12345" 403 times to form a 2015-digit number "$123451234512345 \cdots$". Starting from the left, sequentially delete all digits located in the odd positions of this number to form a new number. Repeat this process of deleting all digits in the odd positions of the newly formed number until only one digit remains. What is the last remaining digit?

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