
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 triangle has its sides in an arithmetic sequence with the common difference $2k$ where $k$ is a positive integer. The lengths of the sides are $b-k$, $b$, and $b+k$, and it is given to be a right triangle. Determine a condition relating $b$ and $k$ for this to be possible.
A) $b = k$   
B) $b = 2k$   
C) $b = 3k$   
D) $b = 4k$

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