
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
Define a sequence  $(a_n)$  recursively by  $a_1=0, a_2=2, a_3=3$  and  $a_n=\max_{0<d<n} a_d \cdot a_{n-d}$  for  $n \ge 4$ . Determine the prime factorization of  $a_{19702020}$ .

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