
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
The first term of the sequence $\{a_n\}$ is 3, and $\{b_n\}$ is an arithmetic sequence, where $b_1=2$, $b_3=6$, and $b_n=a_{n+1}-a_n$ ($n\in\mathbb{N}^*$). Calculate the value of $a_6$.

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