
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 are  $n$  positive integers on the board. We can add only positive integers  $c=\frac{a+b}{a-b}$ , where  $a$  and  $b$  are numbers already writted on the board.  $a)$  Find minimal value of  $n$ , such that with adding numbers with described method, we can get any positive integer number written on the board $b)$  For such  $n$ , find numbers written on the board at the beginning

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