
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 the sequence $\{a_n\}$ satisfies $a_1=1$, $a_2= \dfrac{1}{3}$, and for $n \geq 2, n \in \mathbb{N}^+$, the condition $a_n a_{n-1} + 2a_n a_{n+1} = 3a_{n-1}a_{n+1}$ holds, find the general term $a_n=$ _________.

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