
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
 Navi and Ozna are playing a game where Ozna starts first and the two take turn making moves. A positive integer is written on the waord. A move is to (i) subtract any positive integer at most 2015 from it or (ii) given that the integer on the board is divisible by  $2014$ , divide by  $2014$ . The first person to make the integer  $0$  wins. To make Navi's condition worse, Ozna gets to pick integers  $a$  and  $b$ ,  $a\ge 2015$  such that all numbers of the form  $an+b$  will not be the starting integer, where  $n$  is any positive integer.

Find the minimum number of starting integer where Navi wins.

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