
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
For two sequences $\{a_n\}$ and $\{b_n\}$, where each term is a positive number, and satisfy the conditions that $a_n$, $b_n$, $a_{n+1}$ form an arithmetic sequence, and $b_n$, $a_{n+1}$, $b_{n+1}$ form a geometric sequence, with $a_1=1$ and $a_2=3$, find the general term formula for the sequence $\{a_n\}$.

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