
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
Let $k$ be a positive integer. Bernardo and Silvia play a game where Bernardo starts by writing the smallest perfect cube with $k+2$ digits. On each of Bernardo's turns, after writing a number, Silvia erases the last $k+2$ digits of it. Bernardo then writes the next perfect cube, and Silvia erases the last $k+2$ digits, continuing until the last two numbers that remain on the board differ by at least 3. Let $f(k)$ be the smallest positive integer not written on the board. For k = 1, determine $f(1)$.
A) 145
B) 148
C) 149
D) 150
E) 151

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