
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
Which number is greater:

$$
\underbrace{888 \ldots 88}_{19 \text { digits }} \cdot \underbrace{333 \ldots 33}_{68 \text { digits }} \text { or } \underbrace{444 \ldots 44}_{19 \text { digits }} \cdot \underbrace{666 \ldots 67}_{68 \text { digits }}
$$

and by how much?

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