
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
We define the sequence \(\left(a_{n}\right)_{n \geqslant 0}\) by \(a_{0} = 2\), and for all \(n \geqslant 1\), \(a_{n} = a_{n-1} + l(a_{n-1})\) where \(l(k)\) is the largest prime factor dividing \(k\). Determine all the perfect squares that are terms of the sequence \(\left(a_{n}\right)\).

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