
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
Given an arithmetic sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$, and $\frac{S\_5}{5} - \frac{S\_2}{2} = 3$, find the common difference of the sequence $\{a\_n\}$.

A) $1$
B) $2$
C) $3$
D) $4$

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