
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  $a_1,a_2,\dots, a_{17}$  be a permutation of  $1,2,\dots, 17$  such that  $(a_1-a_2)(a_2-a_3)\dots(a_{17}-a_1)=2^n$  . Find the maximum possible value of positive integer  $n$  .

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