
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
Let  $a_1,a_2,a_3,...$  be a sequence of positive real numbers such that:

(i) For all positive integers  $m,n$ , we have  $a_{mn}=a_ma_n$ (ii) There exists a positive real number  $B$  such that for all positive integers  $m,n$  with  $m<n$ , we have  $a_m < Ba_n$ Find all possible values of  $\log_{2015}(a_{2015}) - \log_{2014}(a_{2014})$ 

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