
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
It is known that the sequence of numbers \(a_{1}, a_{2}, \ldots\) is an arithmetic progression, and the sequence of products \(a_{1}a_{2}, a_{2}a_{3}, a_{3}a_{4}, \ldots\) is a geometric progression. It is given that \(a_{1} = 1\). Find \(a_{2017}\).

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