
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 all values of \( n \) (where \( n \) is a natural number), for which the sum of the first \( n \) terms of the sequence \( a_{k} = 3k^{2} - 3k + 1 \), is equal to the sum of the first \( n \) terms of the sequence \( b_{k} = 2k + 89 \).

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