
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
Estimate the number of primes among the first thousand primes divide some term of the sequence
    \[2^0+1,2^1+1,2^2+1,2^3+1,\ldots.\]
    An estimate of  $E$  earns  $2^{1-0.02|A-E|}$  points, where  $A$  is the actual answer.


*2021 CCA Math Bonanza Lightning Round #5.4*

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