
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  $b$  be a positive integer. Grogg writes down a sequence whose first term is  $1$ .  Each term after that is the total number of digits in all the previous terms of the sequence when written in base  $b$ . For example, if  $b = 3$ , the sequence starts  $1, 1, 2, 3, 5, 7, 9, 12, \dots$ . If  $b = 2521$ , what is the first positive power of  $b$  that does not appear in the sequence?


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