
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
Consider a sequence $\{a_n\}$ with its first term being 3, and let $\{b_n\}$ be an arithmetic sequence. Given that $b_1 = 2$, $b_3 = 6$, and $b_n = a_{n+1} - a_n$ for $n \in \mathbb{N}^*$, determine the value of $a_6$.

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