
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 the smallest integer value of $k$ such that the product $(9)(777\ldots7)$, where the second factor has $k$ digits all being 7, results in a number whose digits sum up to $900$.
A) 97
B) 98
C) 99
D) 100
E) 101

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