
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
Find the smallest possible sum  $a + b + c + d + e$  where  $a, b, c, d,$  and  $e$  are positive integers satisfying the conditions  $\star$  each of the pairs of integers  $(a, b), (b, c), (c, d),$  and  $(d, e)$  are **not** relatively prime $\star$  all other pairs of the five integers **are** relatively prime.

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