
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 sequences $\{a_n\}$ and $\{b_n\}$ satisfy $a_1=1$, and $a_{n+1}$, $1+a_n$ are the two roots of the function $f(x)=x^2-b_nx+a_n$. Find $a_2=$ ______, and when $b_n > \frac{4}{3}$, the maximum value of $n$ is ______.

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