
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
Suppose that $c$ is a positive integer greater than or equal to $2.$ When $256$ is converted to base $c$, the resulting representation has $3$ digits. What is the number of possible values for $c$?

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