
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
The sequence of positive integers  $a_1, a_2, \dots$  has the property that  $\gcd(a_m, a_n) > 1$  if and only if  $|m - n| = 1$ . Find the sum of the four smallest possible values of  $a_2$ .

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