
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
Let the sequence of positive integers $\left\{a_{n}\right\}$ satisfy $a_{n+3}=a_{n+2}\left(a_{n+1}+2a_{n}\right)$ for $n=1,2, \cdots$, and given $a_{6}=2288$. Find $a_{1}, a_{2}, a_{3}$.

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