
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  $a_1 = 1$  and  $a_{n+1} = a_n \cdot p_n$  for  $n \geq 1$  where  $p_n$  is the  $n$ th prime number, starting with  $p_1 = 2$ . Let  $\tau(x)$  be equal to the number of divisors of  $x$ . Find the remainder when  $$ \sum_{n=1}^{2020} \sum_{d \mid a_n} \tau (d) $$  is divided by 91 for positive integers  $d$ . Recall that  $d|a_n$  denotes that  $d$  divides  $a_n$ . 

*Proposed by Minseok Eli Park (wolfpack)*

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