
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 \( S_{b}(n) = b \cdot n + \frac{a+b+c}{3}(S(n) - n \cdot S(1)) \), rewrite it for specific values \( b = 4 \) and \( \frac{a+b+c}{3} = 6 \).

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