
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
For a positive integer  $n$ , let  $d\left(n\right)$  be the number of positive divisors of  $n$  (for example  $d\left(39\right)=4$ ). Estimate the average value that  $d\left(n\right)$  takes on as  $n$  ranges from  $1$  to  $2019$ . An estimate of  $E$  earns  $2^{1-\left|A-E\right|}$  points, where  $A$  is the actual answer.

*2019 CCA Math Bonanza Lightning Round #5.3*

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