
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
A sequence of values in the range \( 0, 1, 2, \ldots, k-1 \) is defined as follows: \( a_1 = 1 \), \( a_n = (a_{n-1} + n) \mod k \). For which \( k \) does the sequence assume all \( k \) possible values?

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