
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 \(\{a_n\}\) be defined by
$$
a_{n+3} = a_{n+2} \left(a_{n+1} + 2a_n\right), \quad n = 1, 2, \ldots
$$
and given that \(a_6 = 2288\). Find \(a_1, a_2,\) and \(a_3\).

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