
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  $(p_1, p_2, \dots) = (2, 3, \dots)$  be the list of all prime numbers, and  $(c_1, c_2, \dots) = (4, 6, \dots)$  be the list of all composite numbers, both in increasing order. Compute the sum of all positive integers  $n$  such that  $|p_n - c_n| < 3$ .

*Proposed by Brandon Wang*

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