
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
There is infinite sequence of composite numbers  $a_1,a_2,...,$  where  $a_{n+1}=a_n-p_n+\frac{a_n}{p_n}$  ;  $p_n$  is smallest prime divisor of  $a_n$ . It is known, that  $37|a_n$  for every  $n$ .
Find possible values of  $a_1$ 

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