
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
Rearrange the 37 different natural numbers $1, 2, 3, \cdots, 37$ into a sequence denoted as $a_{1}, a_{2}, \cdots, a_{37}$ such that $a_{1} = 37, a_{2} = 1$, and the sum $a_{1}+a_{2}+\cdots+a_{k}$ is divisible by $a_{k+1}$ for each $k = 1, 2, \cdots, 36$. Find $a_{3}$ and $a_{37}$.

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