
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
Initially, the numbers 2 and 3 are written down. They are then multiplied, and their product, the number 6, is written down. This process continues by multiplying the two last single-digit numbers: \(3 \cdot 6 = 18\), then \(1 \cdot 8 = 8\), next \(8 \cdot 8 = 64\), and so on. As a result, we get the following sequence of digits:

\[2361886424 \ldots\]

Which digits cannot appear in this sequence? Which digit is in the thousandth place?

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