
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
Arrange the numbers 1, 2, 3, ..., 37 in a row $a_1$, $a_2$, ..., $a_{37}$, where $a_1 = 37$, $a_2 = 1$, and make $a_1 + a_2 + \ldots + a_k$ divisible by $a_{k+1}$ ($k=1, 2, 3, \ldots, 36$).  
(1) Find $a_{37}$.  
(2) Find $a_3$.

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