
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  $a_1$ ,  $a_2$ ,  $\ldots$  be an infinite sequence of (positive) integers such that  $k$  divides  $\gcd(a_{k-1},a_k)$  for all  $k\geq 2$ .  Compute the smallest possible value of  $a_1+a_2+\cdots+a_{10}$ .

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