
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
For any positive integer  $n$ , we define the integer  $P(n)$  by : $P(n)=n(n+1)(2n+1)(3n+1)...(16n+1)$ .

Find the greatest common divisor of the integers  $P(1)$ ,  $P(2)$ ,  $P(3),...,P(2016)$ .

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